Answer
$rs^{10}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
\dfrac{\left( r^{1/5}s^{2/3}\right)^{15}}{r^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{r^{\frac{1}{5}\cdot15}s^{\frac{2}{3}\cdot15}}{r^2}
\\\\=
\dfrac{r^{3}s^{10}}{r^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}
r^{3-2}s^{10}
\\\\=
r^{1}s^{10}
\\\\=
rs^{10}
.\end{array}
