## College Algebra (11th Edition)

$\dfrac{y^{6}}{36x^{4}z^{4}}$
$\bf{\text{Solution Outline:}}$ Use the laws of exponents to simplify the given expression, $(-6x^2y^{-3}z^2)^{-2} .$ $\bf{\text{Solution Details:}}$ Using the extended Power Rule of the laws of exponents which is given by $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to \begin{array}{l}\require{cancel} (-6)^{-2}x^{2(-2)}y^{-3(-2)}z^{2(-2)} \\\\= (-6)^{-2}x^{-4}y^{6}z^{-4} .\end{array} Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{y^{6}}{(-6)^{2}x^{4}z^{4}} \\\\= \dfrac{y^{6}}{36x^{4}z^{4}} .\end{array}