Aus Online Mathematik Brückenkurs 1

By using the power rules, we can rewrite the expression,

\displaystyle \left( \frac{2}{3} \right)^{-3}=\frac{2^{-3}}{3^{-3}}=\frac{\frac{1}{2^{3}}}{\frac{1}{3^{3}}}=\frac{\frac{1}{2^{3}}\centerdot 3^{3}}{\frac{1}{3^{3}}\centerdot 3^{3}}=\frac{\frac{3^{3}}{2^{3}}}{1}=\frac{3^{3}}{2^{3}}

and then carry out the calculation:

\displaystyle \frac{3^{3}}{2^{3}}=\frac{3\centerdot 3\centerdot 3}{2\centerdot 2\centerdot 2}=\frac{27}{8}