Answer
$\dfrac{1}{\left(\sqrt[5]{5y} \right)^{3}}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents and the definition of rational exponents to convert the given expression, $
(5y)^{-3/5}
,$ to radical form.
$\bf{\text{Solution Details:}}$
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{1}{(5y)^{3/5}}
.\end{array}
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}
\dfrac{1}{\left(\sqrt[5]{5y} \right)^{3}}
.\end{array}
