Solution
We want to simplify
[tex](-125a^3)^{\frac{2}{3}}[/tex]Note: Useful Tools
[tex]\begin{gathered} (1).\text{ }(a^mb^n)^{\frac{1}{r}}=a^{m\times\frac{1}{r}}\times b^{n\times\frac{1}{r}} \\ \\ (2).\text{ }-125=-5\times-5\times-5=(-5)^3 \end{gathered}[/tex]So to solve the question
[tex]\begin{gathered} (-125a^3)^{\frac{2}{3}}=(-125\times a^3)^{\frac{2}{3}} \\ \\ (-125a^3)^{\frac{2}{3}}=((-5)^3\times a^3)^{\frac{2}{3}} \\ \\ (-125a^3)^{\frac{2}{3}}=(-5)^{3\times\frac{2}{3}}\times a^{3\times\frac{2}{3}} \\ \\ (-125a^3)^{\frac{2}{3}}=(-5)^2\times a^2 \\ \\ (-125a^3)^{\frac{2}{3}}=25\times a^2 \\ \\ (-125a^3)^{\frac{2}{3}}=25a^2 \end{gathered}[/tex]