Multiplying exponents with different bases. The basic rules for multiplying exponents are given below. \mathtt{\Longrightarrow \ 5^{3} \times 7^{3} \ \ }\\\ \\ \mathtt{\Longrightarrow \ ( 5\times 7)^{3}}\\\ \\ \mathtt{\Longrightarrow \ 35^{3}}, Example 02Multiply \mathtt{-8^{11} \times 5^{11}} Solution \mathtt{\Longrightarrow \ -8^{11} \times 5^{11} \ \ }\\\ \\ \mathtt{\Longrightarrow \ ( -8\times 5)^{11}}\\\ \\ \mathtt{\Longrightarrow \ -40^{11}}, Example 03Multiply \mathtt{10^{-15} \times 6^{-15} \ }, Solution \mathtt{\Longrightarrow \ 10^{-15} \times 6^{-15} \ \ }\\\ \\ \mathtt{\Longrightarrow \ ( 10\times 6)^{-15}}\\\ \\ \mathtt{\Longrightarrow \ 60^{-15}}, Example 04Multiply \mathtt{a^{3} \times b^{3} \ }, \mathtt{\Longrightarrow \ a^{3} \times b^{3} \ \ }\\\ \\ \mathtt{\Longrightarrow \ ( a\times b)^{3}}\\\ \\ \mathtt{\Longrightarrow \ ( ab)^{3}}, The multiplication of exponent with different base and power is done by first finding the individual value of exponent and then multiplying the numbers.Let us understand the concept with the help of example.Example 01Multiply \mathtt{\ 2^{3} \times 5^{2}}. The Multiplying Exponents With Different Bases And The Same Exponent (With Ne | Algebra www.pinterest.com. False, we need to add the powers when the bases are the same. This can be expressed as: If the exponents have coefficients attached to their bases, multiply the coefficients together. The Multiplying Exponents With Different Bases And The Same Exponent www.pinterest.com. 33/2 = (23)3/2 = 63/2 = (63) Here, the bases are a and b and the power is n. When multiplying exponents with different bases and the same powers, the bases are multiplied first. For example, 23 24 = 2(3 + 4)= 27= 128. Example: Multiply 2 3 4 3. Even though the exponents are the same, these cannot be added or subtracted because their bases or exponents are . Learn how to solve the maths problems in different methods with understandable steps. Depending on the base and the power, specific rules apply when multiplying exponents. In order to multiply exponents with different bases and the same powers, the bases are multiplied and the power is written outside the brackets. (i) 23 33 = (2 2 2) (3 3 3) = (2 3) (2 3) (2 3) = 6 6 6 It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to . It is usually a letter like x or y. $\, \therefore \,\,\, 2^3 \times 5^3 \,=\, 10^3$. Multiplying exponents with the same base means when the bases are the same while the exponents are different. For exponents with the same base, we should add the exponents: a n a m = a n+m. Free Exponents Multiplication calculator - Apply exponent rules to multiply exponents step-by-step Learn the why behind math with our certified experts, Multiplying Exponents with Different Base. How to divide exponents. 14 Pictures about Multiplying Exponents With Different Bases and the Same Exponent (All : Homeschool Math Net Worksheets Fraction - 1000 ideas about fractions, Properties Of Exponents Worksheet Answers db-excel.com and also How Do You Multiply And Divide Exponents With . because the bases are not the same (although the exponents are). When multiplying two powers that have the same base ( i i ), you can add the exponents. In this case, find value of exponent \mathtt{2^{3} \&\ 5^{2}} separately and then multiply. (2/3)2 (2/3)5 = (2/3)2+5 = Thus, (2/3)7 = 27/37 = 128/2187. Four to the negative 3 power, that is one over four to the third power, or you could view that as one over four times four times four. To multiply terms with different bases but the same power, raise the product of the bases to the power. So, first, we will solve each term separately and then move further. Manage Cookies, Multiplying exponents with different bases. Compute each term separately if the bases in the terms are not the same. Solution: The variable bases are different and the powers are the same, that is, a17 b17= (a b)17 =(ab)17. Of course, there are other special cases to be aware of. Example: Find the product of (5)3 and (7)4, Solution: The square root bases and the powers are different. Multiplying Exponents With Different Bases and the Same Exponent (All. Since there are different scenarios like different bases or different powers, there are different exponent rules that are applied to solve them. Consider two terms with the same base, that is, an and am. Your answer should contain only positive exponents. . Example: Find the product of (5)2 and (5)7. 103 72 = 1000 49 = 49000. Look at the following examples to learn how to multiply the indices with same powers and different bases for beginners. An exponent is a way of expressing repeated multiplication. An exponent can be defined as the number of times a quantity is multiplied by itself. An exponent is a shorthand notation which tells how many times a number (or expression) is multiplied by itself. Since the bases and the powers are different, we will evaluate them separately, 23 45= 8 1024 = 8192. How do you add exponents with variables? Sometimes we need to multiply negative exponents, or multiply exponents with the same base, or different bases. Thus, 7-2 6-3 = 1/72 1/63= 1/(72 63) 9.45 10-5. But when you multiply and divide, the exponents may be different, and sometimes the bases may be different, too. When the terms with the same base are multiplied, the powers are added, i.e., am an = a{m+n}. For example, consider the below multiplication; \mathtt{\Longrightarrow \ a^{m} \times b^{m}} Note that both the numbers have different . Solution: Here, the fractional bases and the powers are different. The procedure to use the multiplying exponents calculator is as follows: Step 1: Enter the base number and the exponent value in the input field Step 2: Now click the button "Solve" to get the product Step 3: Finally, the product of two number with exponents will be displayed in the output field What is Meant by the Multiplying Exponents? Essentially unknown x (the base) will multiply with it n (exponent) times. Question 1: Simplify or Divide 25 4 /5 4 . It can be written mathematically as an bn = (a b)n, Solution: Here, the bases are different but the powers are the same. According to the rule, we will add the powers, 1045 1039 = 10(45+39) = 1084. For example, 23*24 = 23+4 = 27. Let us see this in the following section. Use the same fundamental procedure to multiply any number of exponents which have different bases but the exponent should be same in the terms. Click the red link to read the same. a n b n = (a b) n. For example, 2 2 3 2 = (2 3) 2 = 6 2 = 36. Example: Solve the exponential equations. SolutionNote that both the multiplication have different base and power. Also, if you find the videos helpful, please like, share, and subscribe! 56/2 = 53 = 125, In general, for any non-zero integer a, a m b m = (ab) m where m is any whole number. An exponent (also called a power) is a symbol used to denote repeated multiplication.For example, {eq}3^7 {/eq} means to multiply 7 copies of the number 3. Multiplying Integer Exponents For integer exponents, three cases are possible: (a) Integer exponents with same base and different power (b) Different base and same power (c) Both base and powers are different Multiplying Integer exponents with same Base When we multiply exponent with same base, we simply add the power of given exponents. Exponent laws are practiced with a partner in this one page document which reviews the rules of multiplying and dividing powers with the same base as well as power to a power. For example, (2 3) 5 = 2 15. Become a problem-solving champ using logic, not rules. Simplify Expressions Using the Product Property of Exponents. In all these cases, we follow different rules. Exponent - The number of times to multiply the base. In order to multiply exponents with different bases and the same powers, the bases are multiplied and the power is written outside the brackets. This means it will be y5 y3 = y5 + 3 = y8. In this video, I teach you how to multiply exponents that have different bases AND different exponents (powers). For example, 3a2 4a3 = (3 4)(a2 a3) = 12a5. The general form of this rule is. Notice that the exponent of the product is the sum of the exponents of the terms. exponents exponent multiplying rational algebra. Example: y2 = yy ( yy means y multiplied by y, because in Algebra putting two letters next to each other means to multiply them) Likewise z3 = zzz and x5 = xxxxx Exponents of 1 and 0 Exponent of 1 When two numbers or variables have different bases, we can multiply the expressions by following some basic exponent rules. When the bases are different and the powers are the same. 1) 42 42 2 . There are a couple playlists attached at the. 1) 42 42 44 2) 4 42 43 3) 32 32 34 4) 2 22 22 25 5) 2n4 5n4 10 n8 6) 6r 5r2 30 r3 7) 2n4 6n4 12 n8 a.) Here, we have two scenarios as given below. Multiplying fractions with exponents with same fraction base: (4/3)3 (4/3)2 = (4/3)3+2 = (4/3)5 = 45 / 35 = 4.214. 3 Enter the base of the second multiplier into the third input box. We can also look at it like this: Multiplication of exponent with different base but same power. When the bases are diffenrent and the exponents of a and b are the same, we can multiply a and b first: a n b n = ( a b) n. Example: 3 2 4 2 = (34) 2 = 12 2 = 1212 = 144. For example, when 2 is multiplied thrice by itself, it is expressed as 2 2 2 = 23. Example 2: Find the product of the following expression: 53 52. = 216 = 14.7. Multiplying fractions with exponents with same exponent: (a / b) n (c / d) n = ((a / b)(c / d)) n, (4/3)3 (3/5)3 = ((4/3)(3/5))3 = (4/5)3 = 0.83 = 0.80.80.8 = 0.512. It is proved in this example that the product of exponential terms which have different bases and same exponents is equal to the product of the bases raised to the power of same exponent. Solution: The variable base is the same, that is, 'a'. To multiply terms containing exponents, the terms must have the same base and/or the same power. Multiplying Powers with Different Base and Same Exponents: If we have to multiply the powers where the base is different but exponents are the same then we will multiply the base. For example, the square root of a positive number a can be expressed as a rational exponent in the following way. In these ways in different cases we can divide and multiply Exponents. Welcome to The Multiplying Exponents With Different Bases and the Same Exponent (With Negatives) (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills.com. You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites. This guideline can be summarized as: a n b n = (a b) n. Example (x3) *( y3) = xxx * yyy = (x y) 3. Example 1: Find the product of (2/3)2 and (15/8)2, Solution: Here, the fractional bases are different but the powers are the same. 2 Enter the exponent of the first multiplier into the second input box. Zero raised to any power (excluding 0) is 0. Multiplying exponents with different bases. an bm = (an) (bm). This relationship applies to multiply exponents with the same base whether the base is a number or a variable: Whenever you multiply two or more exponents with the same base, you can simplify by adding the value of the exponents: Here are a few examples applying the . Multiply the terms by adding the exponents. a) Calculator example #1 Step: X = 5 a = 2 Y= 10 b = 3 x^ {a}\times y^ {b} = 25 \times 1000 = 25000 b) Calculator example #2 Step: X = 1 a = 0 Y= 9 b = 2 (5)4 = 5(2+4)/2 = For example, 2-3 2-9 = 2-(3+9) = 2-12 = 1/212 = 1/4096 0.000244. When the terms with the same base are multiplied, the powers are added. 3. Observe the following exponents to understand how to multiply exponents with different bases and same powers. Solution: Here, the bases are the same. 1. If the bases are the same, then you can simply add the exponents. It is proved in this example that the product of exponential terms which have different bases and same exponents is equal to the product of the bases raised to the power of same exponent. Thus, 6-3 3-3= (6 3)-3 = 18-3 = 1/183 = 1/5832 0.0001715, Solution: Here, both the bases and the negative powers are different. Solved example of multiply powers of same base. Digital Exponent Rules (Law of Exponents)-Multiplying Powers with the Same Base by Teacher Twins $2.00 Google Drive folder Use for Distance Learning. When the variable bases are the same, the powers are added. It tells the number of time the number being multiplied. algebra math exponent rule rules interactive problems notes exponents mathequalslove maths chart list grade notebook teaching adding formulas operations integer. Lesson Summary. It is read as '2 raised to the power of 3'. Here, 2 is the base, and 3 is the power or exponent. So, 2/3 + 3/4 = 17/12. (a) 7 x - 1 = 4. The multiplication of exponent with different base and same power can be done by multiplying the base separately and then inserting the same power.For example, consider the below multiplication; \mathtt{\Longrightarrow \ a^{m} \times b^{m}} Note that both the numbers have different base a & b, but have the same power m.In this case, multiply the individual bases a & b and afterwards insert the power m. The general rule for multiplying exponents with the same base is a1/m a1/n = a (1/m + 1/n). = (3 x 3 x 3 x 3 x 3) 5 x (2 x 2 x 2 x 2 x 2) 5. There are two cases in the given multiplication;(a) the exponent have same power(b) the exponent have different powerWe will discuss both the cases in detail. Example: (3 x 2) 5. Solution: In the given question, the base is the same, that is, 10. For example, (2a2b3)2 = 22 a(22) b(32) = 4a4b6. Yes, expressions with different coefficients can be multiplied. tr\cdot i\cdot n\cdot o\cdot m\cdot i\cdot o tri nomio. To multiply terms with different bases but the same power, raise the product of the bases to the power. When the bases are diffenrent and the exponents of a and b are the same, we can multiply a and b first: When the bases and the exponents are different we have to calculate each exponent and then multiply: For exponents with the same base, we can add the exponents: 2-3 2-4 = 2-(3+4) = 2-7 = 1 / 27 = 1 / (2222222) = 1 / 128 = 0.0078125, 3-2 4-2 = (34)-2 = 12-2 = 1 / 122 = 1 / (1212) = 1 / 144 = 0.0069444, 3-2 4-3 = (1/9) (1/64) = 1 / 576 = 0.0017361. There are some basic rules given below that are used in almost all the cases. \mathtt{\Longrightarrow \ 2^{3} \times \ 5^{2} \ \ }\\\ \\ \mathtt{\Longrightarrow \ 8\ \times \ 25}\\\ \\ \mathtt{\Longrightarrow \ 200\ } Hence, 200 is the solution of given multiplication. When the bases and the negative powers are different. $(1) \,\,\,\,\,\,$ $2^5 \times 3^5 \times 4^5$, $\,=\,$ $(2 \times 2 \times 2 \times 2 \times 2)$ $\times$ $(3 \times 3 \times 3 \times 3 \times 3)$ $\times$ $(4 \times 4 \times 4 \times 4 \times 4)$, $\,=\,$ $2 \times 2 \times 2 \times 2 \times 2$ $\times$ $3 \times 3 \times 3 \times 3 \times 3$ $\times$ $4 \times 4 \times 4 \times 4 \times 4$, $\,=\,$ $(2 \times 3 \times 4)$ $\times$ $(2 \times 3 \times 4)$ $\times$ $(2 \times 3 \times 4)$ $\times$ $(2 \times 3 \times 4)$ $\times$ $(2 \times 3 \times 4)$, $\,\, \therefore \,\,\,\,\,\,$ $2^5 \times 3^5 \times 4^5$ $\,=\,$ ${(2 \times 3 \times 4)}^5$ $\,=\,$ $24^5$. When the fractional bases and the powers are different. Here a and b are the different bases and n is the power of both a and b. You can only multiply terms with exponents when the bases are the same. Observe the below best examples to understand the multiplication of exponential terms having different bases and same exponents. The value of any term with a negative exponent is the reciprocal of the same term with a positive exponent instead. Thus, 2-3 2-9 = 2-(3+9) = 2-12 = 1/212 = 1/4096 0.000244, Solution: Here, the bases are different and the negative powers are the same. -3 -3, we already figured out is positive 9. In other words, we can convert a negative exponent to a positive one by writing the reciprocal of the given term and then we can solve it like a positive term. In this case, the 7 is . When the terms with the same base are multiplied, the powers are added, i.e., a, In order to multiply terms with different bases and the same powers, the bases are multiplied first. Example 03Multiply \mathtt{\ 2^{-2} \times \ 7^{-3}} Solution \mathtt{\Longrightarrow \ 2^{-2} \times \ 7^{-3} \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{2^{2}} \ \times \ \frac{1}{7^{3}}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{4} \times \frac{1}{343}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{4\ \times 343}}\\\ \\ \mathtt{\Longrightarrow \frac{1}{1372}}, Your email address will not be published. Welcome to The Multiplying Exponents With Different Bases and the Same Exponent (All Positive) (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills.com. According to the exponent rule for multiplication with the same base, we add the powers. Worksheets For Negative And Zero Exponents www.homeschoolmath.net. Click the red link to read the same. For example, 34 35 = 3(4+5) = 39. SolutionBoth numbers have different base and power.So we will first find the value of each exponent and then multiply. Multiplying exponents with the same base. Multiplying fractional exponents with same base: Multiplying fractional exponents with different exponents and fractions: 2 3/2 24/3 = (23) I do both positive and negative examples.0:00 - Introduction0:43 - Multip. For example, 23/5 is a fractional exponent. The division of fractional exponents can be classified into two types. The use of multiplying exponents calculator is very simple, mainly in the following steps: 1 Enter the base of the first multiplier into the first input box. In other words, when multiplying exponential expressions with the same base, we write the result with the common base and add the exponents. When exponents with different bases and different powers are multiplied, so each exponent is evaluated separately and then multiplied. In order to multiply exponents with different bases and the same powers, the bases are multiplied and the power is written outside the brackets. So we're going to multiply them together. $(2) \,\,\,\,\,\,$ ${(-2)}^{10} \times {(-3)}^{10} \times {(-4)}^{10} \,=\, {(-24)}^{10}$, $(3) \,\,\,\,\,\,$ ${(0.11)}^5 \times {(0.12)}^5 \times {(0.13)}^5 \,=\, {(0.014916)}^5$, $(4) \,\,\,\,\,\,$ ${\Bigg(\dfrac{2}{3}\Bigg)}^7 \times {\Bigg(\dfrac{4}{5}\Bigg)}^7 \times {\Bigg(\dfrac{6}{9}\Bigg)}^7 \,=\, {\Bigg(\dfrac{48}{135}\Bigg)}^7$, $(5) \,\,\,\,\,\,$ ${(\sqrt{6})}^4 \times {(\sqrt{7})}^4 \times {(\sqrt{8})}^4 \,=\, {(\sqrt{336})}^4$. Here, the bases are a and b. For example, 2-3 can be written as 1/23. When the fractional bases are different but the powers are the same. Have questions on basic mathematical concepts? If the base of a term is a variable, we use the same exponent rules of multiplication that are used for numbers. According to the rules of multiplying exponents, when the bases are the same, we add the powers. RapidTables.com | When exponents are multiplied with parenthesis, the power outside the parenthesis is multiplied with every power inside the parenthesis. This activity has 12 problems that requires students to simplify expressions with variables by using the exponent rules for multiplying powers with the same base. Now, let us use the exponent rules of multiplication that are applicable to expressions in which the bases are square roots. When the square root bases are different and the powers are the same, the bases are multiplied first. Isolate the exponential part of the equation. If the exponents are above the same base, use the rule as follows: x^m x^n = x^ {m + n} xm xn = xm+n So if you have the problem x 3 x 2, work out the answer like this: x^3 x^2 = x^ {3 + 2} = x^5 x3 x2 = x3+2 = x5 When two terms with exponents are multiplied, it is called multiplying exponents. Let us understand these rules with the help of the following examples. Base - The number being multiplied. Students will be asked to simplify exponential expressions and answer word problems involving the laws of exponents. Four to the negative three plus five power which is equal to four to the second power. When multiplying two powers that have the same base ( o o ), you can add the exponents. Multiplying Exponents with Different Bases and with Different Powers. Example 02Multiply \mathtt{6^{-2} \times \ 3^{3}}. Example 1: Find the product of 23 45 using the rules for multiplying exponents. In order to multiply exponents with different bases and the same powers, the bases are multiplied and the power is written outside the brackets. Using the rule, 2 2 2 3 = 2 (2 + 3) = 2 5. You just need to work two terms out individually and multiply their values to get the final product. 1. : 2. : If an exponent has a negative power, you still need to keep the . Consider two expressions with a different base and the same power an and bn. Now, let us understand these rules with the help of the following examples. It can be written mathematically as an bm = (an) (bm), Example: Multiply the expressions: 103 72. 24 22 = (2 2 2 2) (2 2) = 2 2 2 2 2 2 = 26 = 64, Example 2: Find the product of 1045 and 1039. Save my name, email, and website in this browser for the next time I comment. Now, when we need to rewrite a given exponential term as a rational exponent, we multiply the existing power with 1/2. The exponent is used to represent repeated multiplication of number by itself.For example, consider the below multiplication. However, when we multiply exponents with different bases and different powers, each exponent is solved separately and then they are multiplied. Here, exponents are same as 5 but bases are different that's are 3 and 2. 53 52 = 52+3 = 55 = 3125. How many laws are there in exponents? You can divide exponential expressions, leaving the answers as exponential expressions, as long as the bases are the same. Welcome to The Multiplying Exponents With Different Bases and the Same Exponent (All Positive) (B) Math Worksheet from the Algebra Worksheets Page at Math-Drills.com. Whenever we raised raised a negative base to an exponent, if we raise it to an odd exponent, we are going to get a negative value. Therefore, each term will be solved separately. Coefficients can be multiplied together even if the exponents have different bases. document.getElementById( "ak_js" ).setAttribute( "value", ( new Date() ).getTime() ); At the end of the chapter, solved examples are also provided for further clarity. Let us recall the rules for multiplying exponents with the same base and with different bases in the following figure. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to . 2. Need help with exponents (aka - powers)? Round to the hundredths if needed. You can observe in this example that the exponent of product of exponents with same base is equal to the summation of the exponents. . For example, 2^3 * 2^4 = 2^ (3+4) = 2^7. Multiplying exponents with different bases When you multiply numbers with different (not equal) bases and exponents, enter the values and let the calculator do it for you. Nothing combines. 16 Best Images Of Multiplication Math Worksheets Exponents www.worksheeto.com. Exponents Online Worksheet It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to . There are different rules that are used in multiplying exponents. Grade 01 MathGrade 02 MathGrade 03 Math Grade 04 Math Grade 05 MathGrade 06 MathGrade 07 MathGrade 08 MathGrade 09 MathGrade 10 MathGrade 11 MathGrade 12 Math. The general rule is x^a * x^b = x^ (a+b). Let us understand the rules that are applied to multiply fractional exponents with the help of the following table. Different bases, negative exponents, and non-integer exponents can occasionally make it challenging for learners to understand. subtracting decimals tenths horizontally exponents multiplying exponent . Here, we will use: m p n p = (m n) p = (2 4) 3 = 8 3 . When multiplying two exponents with the same base, the result is the same as a term with base and an new exponent created by adding the two exponents in the terms of the problem. Lesson To divide exponents with the same base, we subtract the bottom exponent from the top exponent. $\,=\, $ $(2 \times 2 \times 2) \times (5 \times 5 \times 5)$, $\,=\, $ $2 \times 2 \times 2 \times 5 \times 5 \times 5$, $\,=\, $ $2 \times 5 \times 2 \times 5 \times 2 \times 5$, $\,=\, $ $(2 \times 5) \times (2 \times 5) \times (2 \times 5)$. To simplify a power of a power, you multiply the exponents, keeping the base the same. \mathtt{a^{m} \times b^{m} \ =\ ( a\times b)^{m}} I hope you understood the process. Multiplying exponents with negative powers follows the same set of rules as multiplying exponents with positive powers. Apart from this, one important point to be remembered is that we can convert radicals to rational exponents and then multiply the given expressions. In this article, we'll talk about when to multiply and add exponents. Your answer should contain only positive exponents. Multiplying Exponents with the Same Base. PART 1: https://youtu.be/UCwoYYZ0i-k PART 3: https://youtu.be/Xrdg9TPx8aM PART 4: https://youtu.be/e7DqRw25W_g How do you multiply two numbers that have the . And that's just a straight forward exponent property, but you can also think about why does that actually make sense. Dividing exponents with different bases. If the bases are different, you can not multiply exponents. 5.0. \displaystyle {a}^ {m}\cdot {a}^ {n}= {a}^ {m+n} am an = am+n An exponent (such as the 2 in x2) says how many times to use the variable in a multiplication. To multiply powers of the same base, add the exponents together: If there's more than one base in an expression with powers, you can combine the numbers with the same bases, find the values, and then write them all together. It can be written as a, When the expressions with the same base are multiplied, the powers are added, i.e., a, When the expressions with different bases and the same powers are multiplied, then the common power is written outside the bracket, i.e., a, When the expressions with different bases and different powers are multiplied, each term is evaluated separately and then multiplied, i.e., a. In mathematics, two or more exponential terms which contain different bases and same powers are participated in multiplication. Let us explore some solved examples to understand this better. A best free mathematics education website for students, teachers and researchers. Thus, 21/2 23/2 = 21/2+3/2 = 24/2 = 22 = 4, Example 2: Find the product of 21/2 and 31/2, Solution: Here, the bases are different but the fractional powers are the same.

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