Simplifying algebraic fraction, exponents

Question

Would someone be able to tell me how $$\bigg( \frac{5}{a^4} \bigg)^{-3}$$ gets simplified to $$\frac{a^{12}}{125}?$$

Thank you!

Answer 1

Here is a dirty but quick way as a rule of thumb: we have $$ \bigg( \frac{5}{a^{4}} \bigg)^{-3} = \bigg( \frac{a^{4}}{5} \bigg)^{3} = \frac{a^{12}}{125} $$

I use "dirty" here because the number $a$ should be $\neq 0$.

Answer 2

You have:

$$ \left(\frac{5}{a^4}\right)^{-3}=\left(\frac{5^{-3}}{a^{-12}}\right)=\left(\frac{a^{12}}{5^3}\right)=\frac{a^{12}}{125} $$