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\frac{1}{\left(-4\right)^{5}}
Rewrite \left(-4\right)^{8} as \left(-4\right)^{3}\left(-4\right)^{5}. Cancel out \left(-4\right)^{3} in both numerator and denominator.
\frac{1}{-1024}
Calculate -4 to the power of 5 and get -1024.
-\frac{1}{1024}
Fraction \frac{1}{-1024} can be rewritten as -\frac{1}{1024} by extracting the negative sign.