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

$(\frac{4}{5})^{-3}=\frac{5^3}{4^3}^{}^{}$

this will be equivalent to prove that:

$4^3\times(\frac{4}{5})^{-3}=5^3$

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

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