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 - 7-2 Multiplying Powers With the Same Base - Practice and Problem-Solving Exercises - Page 430: 35


The answer is $a^{\frac{1}{6}}$

Work Step by Step

To solve this $a^{\frac{2}{3}}$$\times$$a^{x}$ = $a^{\frac{5}{6}}$ $a^{x}$ = $\frac{a^{\frac{5}{6}}}{a^{\frac{2}{3}}}$ $a^{x}$ = $a^{\frac{5}{6}-\frac{2}{3}}$ $a^{x}$ = $a^{\frac{5}{6}-\frac{4}{6}}$ $a^{x}$ = $a^{\frac{1}{6}}$ --> since bases are equal, make the exponents equal x = $\frac{1}{6}$ Therefore the missing part is $a^{\frac{1}{6}}$.
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