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\left(\left(\frac{1}{2}\right)^{-2}\right)^{-2}
Use the rules of exponents to simplify the expression.
\left(\frac{1}{2}\right)^{-2\left(-2\right)}
To raise a power to another power, multiply the exponents.
\left(\frac{1}{2}\right)^{4}
Multiply -2 times -2.
\frac{1}{16}
Raise \frac{1}{2} to the power 4.