Question

Simplificar:
$\sqrt[n]{20/ (4^{n+2}+ 2^{n+2})}$

Answer 1

$\sqrt[n]{\frac{20}{(4^{n+2}+2^{n+2})}}=\\\\\\\sqrt[n]{\frac{20}{\left[(2^2)^{n+2}+2^{n+2}\right]}}=\\\\\\\sqrt[n]{\frac{20}{(2^{2n+4}+2^{n+2})}}=\\\\\\\sqrt[n]{\frac{20}{2^2(2^{2n+2}+2^n)}}=\\\\\\\sqrt[n]{\frac{5}{2^{2n+2}+2^n}}=\\\\\\\sqrt[n]{\frac{5}{2^n(2^{n+2}+1)}}$