Question

What is the simplest radical form of the expression?

Answer 1

$\bf (x^2y^8)^{\frac{2}{3}}\implies \left( x^{2\cdot \frac{2}{3}}y^{8\cdot \frac{2}{3}} \right)\implies x^{\frac{4}{3}}y^{\frac{16}{3}}\implies x^{\frac{3}{3}+\frac{1}{3}}y^{\frac{15}{3}+\frac{1}{3}}\implies x^{1+\frac{1}{3}}y^{5+\frac{1}{3}} \\\\\\ x^1\cdot x^{\frac{1}{3}}\cdot y^5\cdot y^{\frac{1}{3}}\implies x^1\cdot y^5\cdot x^{\frac{1}{3}}\cdot y^{\frac{1}{3}}\implies xy^5\sqrt[3]{x}\sqrt[3]{y}\implies xy^5 \sqrt[3]{xy}$