When simplified, (-(1)/(125))^-(2)/(3) becomes:

1961 AMC 12 Problem 1

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When simplified,

\left(-\dfrac{1}{125}\right)^{-\frac{2}{3}}

becomes:

\dfrac1{25}

-\dfrac1{25}

25

-25

25\sqrt{-1}

Apply the cube root before squaring

The negative exponent then takes the reciprocal

Because the cube root is real,

\left(-\frac1{125}\right)^{\frac{2}{3}} =\left(-\frac15\right)^2=\frac1{25}.

The negative exponent takes the reciprocal, giving

25.

Therefore, the correct answer is C.