## Intermediate Algebra for College Students (7th Edition)

Published by Pearson

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

#### Answer

$x^9y^{12}$

#### Work Step by Step

RECALL: (i) The quotients-to-powers rule states that: $(\frac{a}{b})^n=\frac{a^n}{b^n}$ (ii) The power-rule states that $(a^m)^n=a^{mn}$ (iii) The negative-exponent rule states that: $a^{-m}=\dfrac{1}{a^m}$ and $\dfrac{1}{a^{-m}} = a^m$ Use the quotients-to-powers rule to find: $=\dfrac{(x^3)^3}{(y^{-4})^3}$ Use the power rule to find: $\\=\dfrac{x^{3(3)}}{y^{-4(3)}} \\=\dfrac{x^{9}}{y^{-12}}$ Use the negative-exponent rule to find: $=\dfrac{x^9}{\frac{1}{y^{12}}} \\=x^9 \cdot \frac{y^{12}}{1} \\=x^9y^{12}$

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