Answer
$\color{blue}{15\sqrt[3]{75}}$
Work Step by Step
Note that $25=5^2$, $(-3)^4=81$ and $81=3^4$.
Thus, the given expression is equivalent to:
$=\sqrt[3]{5^2(81)(5^3)}
\\=\sqrt[3]{5^2\cdot 3^4\cdot 5^3}$
Use the rule $a^m\cdot a^n = a^{m+n}$ to obtain:
$=\sqrt[3]{3^4\cdot5^{2+3}}
\\=\sqrt[3]{3^4\cdot 5^5}$
Factor the radicand so that at least one factor is a perfect cube to obtain:
$=\sqrt[3]{((3^3\cdot5^3)(3\cdot5^2)}
\\=\sqrt[3]{(3^3\cdot5^3)(3\cdot25)}
\\=\sqrt[3]{(3^3\cdot5^3)(75)}$
Bring out the cube root of the perfect cube factors to obtain:
$=3\cdot5\sqrt[3]{75}
\\=\color{blue}{15\sqrt[3]{75}}$
