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: 29



Work Step by Step

$(y^{2}z^{-3})^{\frac{1}{6}}(y^{3})^{2}$ (Raise the factor of $y^{2}z^{-3}$ to the $\frac{1}{6}$ power. Multiply the exponents of a power raised to a power) $y^{2\times\frac{1}{6}}z^{-3\times\frac{1}{6}}y^{3\times2}$ (Simplify) $y^{\frac{1}{3}}z^{-\frac{1}{2}}y^{6}$ (Add the exponents of the same base) $y^{\frac{1}{3}+6}z^{-\frac{1}{2}}$ (Make 6 into a fraction with the same denominator) $y^{\frac{1}{3}+\frac{18}{3}}z^{-\frac{1}{2}}$ (Simplify) $y^{\frac{19}{3}}z^{-\frac{1}{2}}$ (Because z has a negative exponent, it must go on the bottom of the fraction) $\frac{y^{\frac{19}{3}}}{z^{\frac{1}{2}}}$
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