Question

Simplify $\sqrt[3]{\left(3 \dfrac{3}{8} x^{12} y^{-6}\right)^{2}}$  without using a calculator.

Answer 1

$\sqrt[3]{\left(3 \frac{3}{8} x^{12} y^{-6}\right)^{2}}$

$=\left(\frac{27}{8} x^{12} y^{-6}\right)^{\frac{2}{3}}$

$=\left(\frac{3^{3} x^{12}}{2^{3} y^{6}}\right)^{\frac{2}{3}}$

$=\frac{3^{3 \times \frac{2}{3}} x^{12 \times \frac{2}{3}}}{2^{3 \times \frac{2}{3}} y^{6 \times \frac{2}{3}}}=\frac{3^{2} x^{8}}{2^{2} y^{4}}=\frac{9 x^{8}}{4 y^{4}}$