Answer
$\color{blue}{rs^{10}}$
Work Step by Step
RECALL:
(1) $a^m \cdot a^n = a^{m+n}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
(3) $a^{1/n} = \sqrt[n]{a}$
(4) When $n$ is odd, $\sqrt[n]{a^n}=a$
(5) $a^{m/n} = \left(\sqrt[n]{a}\right)^m$
(6) $(ab)^m=a^mb^m$
(7) $(a^m)^n=a^{mn}$
Use rule (6) above to obtain:
$=\dfrac{(r^{1/5})^{15}(s^{2/3})^{15}}{r^2}$
Use rule (7) above to obtain:
$=\dfrac{r^{(1/5) \cdot 15}s^{(2/3) \cdot 15}}{r^2}
\\=\dfrac{r^3y^{10}}{r^2}$
Use rule (2) above to obtain:
$=r^{3-2}s^{10}
\\=\color{blue}{rs^{10}}$
