Działania na potęgach.

[jpb]

Oblicz:
\(\displaystyle{ \left(\frac{4}{5} \right)^{-7} \cdot \left(5 ^{-5} : 4 ^{-6} \right)}\)
Jakimś cudem ciągle wychodzi mi \(\displaystyle{ \frac{25}{64}}\)

[kerajs]

\(\displaystyle{ \left(\frac{4}{5} \right)^{-7} \cdot \left(5 ^{-5} : 4 ^{-6} \right)=\left(\frac{5}{4} \right)^{7} \cdot \left( \left(\frac{1}{5} \right)^{5} : \left(\frac{1}{4} \right) ^{6} \right)=\frac{5^7}{4^7}\cdot \left(\frac{1}{5^5} \cdot 4 ^{6} \right)= \frac{25}{4}}\)