If 10^2y=25, then 10^-y equals:

1956 AMC 12 Problem 18

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18.

10^{2y}=25,

then

10^{-y}

equals:

-\dfrac15

\dfrac1{625}

\dfrac1{50}

\dfrac1{25}

\dfrac15

Write

10^{2y}

(10^y)^2

The quantity

10^y

is positive

We have

(10^y)^2=25.

Since

10^y

is positive,

10^y=5.

Taking the reciprocal gives

10^{-y}=\frac{1}{5}.

Thus, the correct answer is E.