Question

\[ \sqrt[3]{a^6 b^{-4}} = a^x b^{2y} \]

Solution

\[ (a^6 b^{-4})^{1/3} = a^x b^{2y} \] \[ = a^{6/3} \cdot b^{-4/3} \] \[ = a^2 \cdot b^{-4/3} \] \[ a^x b^{2y} = a^2 b^{-4/3} \] \[ x = 2,\quad 2y = -\frac{4}{3} \] \[ y = -\frac{2}{3} \]

Answer

\[ \boxed{x = 2,\quad y = -\frac{2}{3}} \]

Next Question / Full Exercise