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\left(\left(-4\right)^{-2}\right)^{3}
Use the rules of exponents to simplify the expression.
\left(-4\right)^{-2\times 3}
To raise a power to another power, multiply the exponents.
\left(-4\right)^{-6}
Multiply -2 times 3.
\frac{1}{4096}
Raise -4 to the power -6.