Answer
$\sqrt[8]{9^5q^5}-\sqrt[3]{4x^2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the definition of rational exponents to convert the given expression, $
(9q)^{5/8}-(2x)^{2/3}
,$ to radical form. Then use the laws of exponents to simplify the resulting expression.
$\bf{\text{Solution Details:}}$
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[8]{(9q)^5}-\sqrt[3]{(2x)^2}
.\end{array}
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}
\sqrt[8]{9^5q^5}-\sqrt[3]{2^2x^2}
\\\\=
\sqrt[8]{9^5q^5}-\sqrt[3]{4x^2}
.\end{array}
