From Förberedande kurs i matematik 1

The whole expression consists of factors having a base of \displaystyle 5;

so the power rules can be use to simplify the expression first:

\displaystyle \begin{align} & \frac{5^{12}}{5^{-4}}\centerdot \left( 5^{2} \right)^{-6}=\frac{5^{12}}{5^{-4}}\centerdot 5^{2\centerdot \left( -6 \right)}=\frac{5^{12}}{5^{-4}}\centerdot 5^{-12}=\frac{5^{12}\centerdot 5^{-12}}{5^{-4}} \\ & \\ & =\frac{5^{12-12}}{5^{-4}}=\frac{5^{0}}{5^{-4}}=5^{0-\left( -4 \right)}=5^{4}=5\centerdot 5\centerdot 5\centerdot 5=625 \\ \end{align}