# Chapter 7 - Algebraic Fractions - 7.1 - Simplifying Algebraic Fractions - Problem Set 7.1: 11

$\frac{4xy}{9z}$

#### Work Step by Step

We use the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$ to help us cancel out common factors in the numerator and denominator: $\frac{32xy^{2}z^{3}}{72yz^{4}}$ =$\frac{32}{72}\times x\times\frac{y^{2}}{y}\times\frac{z^{3}}{z^{4}}$ =$\frac{4}{9}\times x\times y^{2-1}\times z^{3-4}$ =$\frac{4}{9}\times x\times y^{1}\times z^{-1}$ =$\frac{4}{9}\times x\times y^{1}\times \frac{1}{z^{1}}$ =$\frac{4xy}{9z}$

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