Question

Prove that (4/5)^-3 = 5^3/4^3, without using the exponent law (x/y)^a = x^a /y^a.

Answer 1

We need to prove that

`((4)/(5))^(-3)=(5^3)/(4^3)^{}^{}`

this will be equivalent to prove that:

`4^3*((4)/(5))^(-3)=5^3`

so let's start from the left side of the previous equality and try to obtain the right side: