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