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\frac{1}{\left(-\frac{1}{5}\right)^{2}}
Rewrite \left(-\frac{1}{5}\right)^{7} as \left(-\frac{1}{5}\right)^{5}\left(-\frac{1}{5}\right)^{2}. Cancel out \left(-\frac{1}{5}\right)^{5} in both numerator and denominator.
\frac{1}{\frac{1}{25}}
Calculate -\frac{1}{5} to the power of 2 and get \frac{1}{25}.
1\times 25
Divide 1 by \frac{1}{25} by multiplying 1 by the reciprocal of \frac{1}{25}.
25
Multiply 1 and 25 to get 25.