Przykład 1. Oblicz:

a) ${\left(\frac{3}{2}\right)}^{-2}={\left(\frac{2}{3}\right)}^2=\frac{4}{9}$

b) ${\left(\frac{1}{64}\right)}^{-\frac{2}{3}}=64^{\frac{2}{3}}={\left(\sqrt[3]{64}\right)}^2=4^2=16$

c) $\sqrt[3]{7}\cdot \sqrt[3]{49}=\sqrt[3]{7\cdot 49}=\sqrt[3]{7\cdot 7^2}=\sqrt[3]{7^3}=7$

d) $\frac{{\left(9^{\frac{1}{3}}\right)}^2\cdot 9^{-\frac{1}{6}}}{36^{-\frac{1}{3}}:{\left(\frac{1}{6}\right)}^{-\frac{1}{3}}}=\frac{9^{\frac{2}{3}}\cdot 9^{-\frac{1}{6}}}{{\left(36:\frac{1}{6}\right)}^{-\frac{1}{3}}}=\frac{9^{\frac{2}{3}+\left(-\frac{1}{6}\right)}}{{\left(36\cdot 6\right)}^{-\frac{1}{3}}}=$
$=\frac{9^{\frac{4}{6}-\frac{1}{6}}}{216^{-\frac{1}{3}}}=\frac{9^{\frac{3}{6}}}{\frac{1}{\sqrt[3]{216}}}=\frac{9^{\frac{1}{2}}}{\frac{1}{6}}=\frac{\sqrt{9}}{\frac{1}{6}}=3:\frac{1}{6}=3\cdot \frac{6}{1}=18$

e) $\frac{625^{-1}\cdot \sqrt{5}}{125^{-2}\cdot \sqrt[4]{25}}=\frac{{\left(5^4\right)}^{-1}\cdot 5^{\frac{1}{2}}}{{\left(5^3\right)}^{-2}\cdot 5^{\frac{2}{4}}}=\frac{5^{-4}\cdot 5^{\frac{1}{2}}}{5^{-6}\cdot 5^{\frac{1}{2}}}=\frac{5^{-3\frac{1}{2}}}{5^{-5\frac{1}{2}}}=$
$=5^{-\frac{7}{2}-\left(-\frac{11}{2}\right)}=5^{-\frac{7}{2}+\frac{11}{2}}=5^{\frac{4}{2}}=5^2=25$