How do you simplify the expression [(z^-2)^2]^3 using the properties?

Feb 2, 2018

$\frac{1}{z} ^ 12$

Explanation:

First, ${z}^{-} n = \frac{1}{z} ^ n$

So it becomes ${\left[\frac{1}{z} ^ \left({2}^{2}\right)\right]}^{3}$

Becuase ${1}^{n} = 1$ and ${\left(\frac{a}{b}\right)}^{n} = {a}^{n} / {b}^{n}$

And ${\left({a}^{b}\right)}^{c} = {a}^{b c}$ Makes the equation

${\left[\frac{1}{z} ^ 4\right]}^{3}$

Using the last three again, we get

$\frac{1}{z} ^ 12$