<s>[INST] How to simplify $\frac{1}{3^{-2}}$ properly? Saw how it was simplified and I was wondering what allows you to rewrite this as $3^2 = 9$? 
 [/INST] $\frac{1}{3^{-2}}=\frac{1}{3^{-2}}\cdot 1 = \frac{1}{3^{-2}}\cdot\frac{3^2}{3^2}=\frac{1\cdot 3^2}{3^{-2}\cdot 3^2}=\frac{3^2}{3^{-2+2}}=\frac{3^2}{3^0}=\frac{3^2}{1}=3^2$
In general, you can skip many of these steps and use the result $x^n=\frac{1}{x^{-n}}$ for any nonzero $x$.
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