Answer
$x^{3}y^{8}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
