# Chapter 4 - Polynomials - 4.1 Exponents and Their Properties - 4.1 Exercise Set - Page 236: 84

$\dfrac{x^{20}}{81y^{12}}$

#### Work Step by Step

Using $\left(\dfrac{a}{b}\right)^x=\dfrac{a^x}{b^x}$, then the expression, $\left(\dfrac{x^5}{-3y^3}\right)^4$, simplifies to \begin{array}{l}\require{cancel} \dfrac{(x^5)^4}{(-3y^3)^4} .\end{array} Using $(a^x)^y=a^{xy}$, then the given expression, $\dfrac{(x^5)^4}{(-3y^3)^4}$, simplifies to \begin{array}{l}\require{cancel} \dfrac{x^{5(4)}}{(-3)^4y^{3(4)}} \\\\= \dfrac{x^{20}}{81y^{12}} .\end{array}

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