Propriedade usada
[tex]\sqrt[a]{b^c}=b^{\frac{c}{a}}[/tex]
Solução :
[tex]\sqrt[16]{2^8}=\sqrt[x]{2^4}\\\\2^{\frac{8}{16}}=2^{\frac{4}{x}}\quad\mbox{se as bases sao iguais entao os expoentes tambem sao iguais, logo}\\\\\dfrac{8}{16}=\dfrac{4}{x}\\\\8x=4\cdot16\\\\x=\dfrac{64}{8} \\\\\boxed{\boxed{x=8}}[/tex]
