Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 1 - Section 1.6 - Properties of Integral Exponents - Exercise Set - Page 81: 143


$$(\frac{x^{2}}{y^{6}})^3 = \frac{x^{2\cdot3}}{y^{6\cdot3}} = \frac{x^{6}}{y^{18}}$$

Work Step by Step

Quotient to Power rule: $(\frac{a}{b})^{n} = \frac{a^n}{b^n}$ where $b\ne0$, states that when a quotient is raised to a power, raise the numerator to that power and divide by the denominator raised to the same power. For example, consider the expression $(\frac{x^{2}}{y^{6}})^3$. To simplify, raise the numerator, $x^{2}$ and the denominator, ${y^{6}}$ by $3$. Thus, $$(\frac{x^{2}}{y^{6}})^3 = \frac{x^{2\cdot3}}{y^{6\cdot3}} = \frac{x^{6}}{y^{18}}$$
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