Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 7 - Exponents and Exponential Functions - 7-3 More Multiplication Properties of Exponents - Practice and Problem-Solving Exercises - Page 437: 57



Work Step by Step

When we raise a power to a power, we multiply the powers together and keep the base. Let's multiply the exponent of each term by the exponent outside of the parentheses: $(-2a^{\frac{2}{3}}b)^{3}(ab^{\frac{1}{3}})^{3}$ Multiply the exponents: $((-2)^3a^{({\frac{2}{3}})(3)}b^{3})(a^{3}b^{(\frac{1}{3})(3)})$ Simplify the expression: $-8a^{2}b^{3}a^{3}b^{1}$ When multiplying exponents with the same base, we add the exponents and keep the same base: $-8a^{5}b^{4}$
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