Respuesta:
Explicación paso a paso:
[tex]\sqrt[n]{\frac{2^{n+2} }{\sqrt[n+2]{2^{2n+n^{2} } } } }[/tex]
trabajando aparte con la raíz interior
[tex]\sqrt[n+2]{2^{2n+n^{2} } }[/tex]
aplicando [tex]\sqrt[a]{x^{b} } = x^{\frac{b}{a} }[/tex]
[tex]2^{ \frac{ 2n+n^{2} }{n+2} }[/tex] = [tex]2^{ \frac{ n(2+n) }{n+2} } = 2^{n}[/tex]
reemplaza
[tex]\sqrt[n]{\frac{2^{n+2} }{2^{n}} }[/tex] = [tex]\sqrt[n]{2^{n+2 -n} }[/tex] = [tex]\sqrt[n]{2^{2} }[/tex] = [tex]\sqrt[n]{4}[/tex]
[tex]\sqrt[n]{\frac{2^{n+2} }{\sqrt[n+2]{2^{2n+n^{2} } } } } = \sqrt[n]{4}[/tex]
