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

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Answer 1 · 2018-02-02T23:03:15

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

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

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

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

And ${(a^{b})}^{c} = a^{b c}$ $(a^b)^c=a^(bc)$ Makes the equation

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

Using the last three again, we get

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

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