From Förberedande kurs i matematik 1

Before we begin to calculate, it is worthwhile looking at the expression first and investigating whether it can be simplified using the power rules, so as to reduce the arithmetical work somewhat.

Because \displaystyle 9=3\cdot 3=3^{2}, we have

\displaystyle 9^{-2}=\bigl( 3^{2} \bigr)^{-2}=3^{2\cdot (-2)}=3^{-4}

and thus

\displaystyle 3^{5}\cdot 9^{-2}=3^{5}\cdot 3^{-4}=3^{5-4}=3^1=3\,.