Question

¿Simplificar esta expresión?

Answer 1

$\sqrt[n]{ \frac{ (2^{6})^{n}+ (2^{4}) ^{2n} }{ (2^{3} )^{n}+ (2^{5} )^{n} } }$
$\sqrt[n]{ \frac{ 2^{6n}+ 2^{8n} }{ 2^{3n}+ 2^{5n} } }$
factorizando
$\sqrt[n]{ \frac{ 2^{6n}(1+2^{2n} ) }{ 2^{3n}(1+ 2^{2n} ) } }$
simplificando$\sqrt[n]{ \frac{ 2^{6n} }{2 ^{3n} } } = \sqrt[n]{ 2^{3n} }= 2^{3}=8$