[tex]\left( \dfrac{4}{5} \right)^{-3}[/tex]
There are a few ways to approach this.
My preference is to apply that -3 exponent to both the top and the bottom:
[tex]\left( \dfrac{4}{5} \right)^{-3} = \dfrac{4^{-3}}{5^{-3}}[/tex]
I'd do that the same way, no matter whether the exponent outside was a postive or negative number.
Since it is a negative number, I remember that negative exponents mean that factor is on the wrong side of the fraction. So anything with a negative exponent will move to the other side.
[tex]\dfrac{4^{-3}}{5^{-3}} = \dfrac{5^3}{4^3}[/tex]
Be sure to make the exponents' signs change when you move them to the other side of the fraction.
Finally I would evaluate [tex]5^3[/tex] and [tex]4^3[/tex] on their own to get my answer.
[tex]\dfrac{5^3}{4^3} = \dfrac{5 \cdot 5 \cdot 5}{4\cdot 4 \cdot 4} = \dfrac{~~~?~~~}{?}[/tex]
