Question

(√2/5)^8/(√2/5)^(1/3)​

Answer 1

$\displaystyle \left(\frac{\sqrt{2}}{5}\right)^8 \div \left(\frac{\sqrt{2}}{5}\right)^{\frac{1}{3}} \\ \\ \\ \\ \left(\frac{\sqrt{2}}{5}\right)^{8-\frac{1}{3}}\ \ \ \ \ \ \ \ [\because\ a^m \div a^n = a^{m-n}] \\ \\ \\ \\ \left(\frac{\sqrt{2}}{5}\right)^{7\frac{2}{3}} \\ \\ \\ \\ \left(\frac{\sqrt{2}}{5}\right)^{\frac{23}{3}} \\ \\ \\ \\ \sqrt[3]{\left(\frac{\sqrt{2}}{5}\right)^{23}}$