Question

A. Simplify the Rational Exponent:1. (-125 a^3)^(2/3)

Answer 1

We want to simplify

`(-125a^3)^{(2)/(3)}`

Note: Useful Tools

`\begin{gathered} (1).\text{ }(a^mb^n)^{(1)/(r)}=a^{m*(1)/(r)}* b^{n*(1)/(r)} \\ \\ (2).\text{ }-125=-5*-5*-5=(-5)^3 \end{gathered}`

So to solve the question

`\begin{gathered} (-125a^3)^{(2)/(3)}=(-125* a^3)^{(2)/(3)} \\ \\ (-125a^3)^{(2)/(3)}=((-5)^3* a^3)^{(2)/(3)} \\ \\ (-125a^3)^{(2)/(3)}=(-5)^{3*(2)/(3)}* a^{3*(2)/(3)} \\ \\ (-125a^3)^{(2)/(3)}=(-5)^2* a^2 \\ \\ (-125a^3)^{(2)/(3)}=25* a^2 \\ \\ (-125a^3)^{(2)/(3)}=25a^2 \end{gathered}`