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\frac{1}{\left(-4\right)^{5}}
Use the rules of exponents to simplify the expression.
\left(-4\right)^{5\left(-1\right)}
To raise a power to another power, multiply the exponents.
\left(-4\right)^{-5}
Multiply 5 times -1.
-\frac{1}{1024}
Raise -4 to the power -5.