[tex]~\hspace{7em}\textit{rational exponents} \\\\ ~\hspace{7em}a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( x^2y^8 \right)^{\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 \sqrt[3]{x^4}\sqrt[3]{y^{16}}\implies \sqrt[3]{x^4y^{16}} \\\\\\ \sqrt[3]{x^{3+1}y^{3+3+3+3+3+1}}\implies \sqrt[3]{x^3xy^3y^3y^3y^3y^3y} \\\\\\ xyyyyy\sqrt[3]{xy}\implies xy^5\sqrt[3]{xy}[/tex]
