Question

What is the simplest radical form of the expression? (x^3y^5)^(4/3)

Answer 1

$\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x^3y^5)^{\frac{4}{3}}\implies \left( x^{3\cdot \frac{4}{3}}y^{5\cdot \frac{4}{3}} \right)\implies x^4y^{\frac{20}{3}}\implies x^4 y^{\frac{18}{3}+\frac{2}{3}}\implies x^4 y^{\frac{18}{3}} y^{\frac{2}{3}} \\\\\\ x^4y^6 y^{\frac{2}{3}}\implies x^4y^6\sqrt[3]{y^2}$