Answer
$\color{blue}{25}$
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) $a^{m/n} = \left(\sqrt[n]{a}\right)^m$
Use rule (2) above to obtain:
$=125^{7/3-5/3}
\\=125^{2/3}$
Use rule (5) above to obtain:
$=\left(\sqrt[3]{125}\right)^2
\\=\left(\sqrt[3]{5^3}\right)^2$
Use rule (4) above to obtain:
$\\=5^2
\\=\color{blue}{25}$
