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3a^{2}\times 5^{-2}a^{-2}
Expand \left(5a\right)^{-2}.
3a^{2}\times \frac{1}{25}a^{-2}
Calculate 5 to the power of -2 and get \frac{1}{25}.
\frac{3}{25}a^{2}a^{-2}
Multiply 3 and \frac{1}{25} to get \frac{3}{25}.
\frac{3}{25}
Multiply a^{2} and a^{-2} to get 1.