Question

What is the simplest radical form of expression?

Answer 1

`~\hspace{7em}\textit{rational exponents} \\\\ ~\hspace{7em}a^{( n)/( m)} \implies \sqrt[ m]{a^ n} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( x^2y^8 \right)^{(2)/(3)}\implies \left(x^{2\cdot (2)/(3)}y^{8\cdot (2)/(3)} \right)\implies x^{(4)/(3)}y^{(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}`