Intermediate Algebra (12th Edition)

$x^{3}y^{8}$
$\bf{\text{Solution Outline:}}$ Use the laws of exponents to simplify the given expression, $\dfrac{\left( x^{1/4}y^{2/5}\right)^{20}}{x^2} .$ $\bf{\text{Solution Details:}}$ 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} \dfrac{x^{\frac{1}{4}\cdot20}y^{\frac{2}{5}\cdot20}}{x^2} \\\\= \dfrac{x^{5}y^{8}}{x^2} .\end{array} Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to \begin{array}{l}\require{cancel} x^{5-2}y^{8} \\\\= x^{3}y^{8} .\end{array}