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9a^{2}\times 6^{-2}a^{-2}
Expand \left(6a\right)^{-2}.
9a^{2}\times \frac{1}{36}a^{-2}
Calculate 6 to the power of -2 and get \frac{1}{36}.
\frac{1}{4}a^{2}a^{-2}
Multiply 9 and \frac{1}{36} to get \frac{1}{4}.
\frac{1}{4}
Multiply a^{2} and a^{-2} to get 1.