$$ =\left(4^{-1}\right)^{-2} $$ $$ ==4^{2} $$ or 16

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$$ \left(4^{-1}\right)^{-2} = 16 $$ To simplify the expression $$ \left(4^{-1}\right)^{-2} $$, we can follow these steps: 1. Start with the inner expression: $$ 4^{-1} $$ is equal to $$ \frac{1}{4} $$. 2. Now, raise $$ \frac{1}{4} $$ to the power of $$-2$$: $$ \left(4^{-1}\right)^{-2} = \left(\frac{1}{4}\right)^{-2} $$ 3. When you raise a fraction to a negative exponent, you can take the reciprocal and change the sign of the exponent: $$ \left(\frac{1}{4}\right)^{-2} = \left(4\right)^{2} $$ 4. Now calculate $$ 4^{2} $$: $$ 4^{2} = 16 $$ Thus, $$ \left(4^{-1}\right)^{-2} = 4^{2} = 16 $$. So, the answer is indeed $$ 16 $$.

\( =\left(4^{-1}\right)^{-2} \) \( ==4^{2} \) or 16

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\( =\left(4^{-1}\right)^{-2} \) \( ==4^{2} \) or 16

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