Question

Simplify (square root 3)(5 square root 3)

Answer 1

`\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{( n)/( m)} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-( n)/( m)} \implies \cfrac{1}{a^{( n)/( m)}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( √(3) \right)\left( \sqrt[5]{3} \right)\implies \left( \sqrt[2]{3^1} \right)\left( \sqrt[5]{3^1} \right)\implies 3^{(1)/(2)}\cdot 3^{(1)/(5)}\implies 3^{(1)/(2)+(1)/(5)}\implies 3^{(5+2)/(10)}\implies 3^{(7)/(10)}`