Question

Simplify:
${\{\sqrt[3]{34}\times \frac{1}{\sqrt[6]{68}}\sqrt[12]{122^{-1}}\}}^{12}$

Answer 1

$(4^{1/3}\times \frac{1}{8^{1/6}}{2}^{-1/12}{)}^{12}$

$=4^{12/3}\times \frac{1}{8^{12/16}}{2}^{-12/12}$ since $a^m{)}^n=a{=}^{mn}$

$=4^4\times \frac{1}{8^2}{2}^{-12/12}$

$=(2^2{)}^4\times (2^{-3}{)}^2{2}^{-1}$ since $1/a^m=a^{-m}$

$=2^8-6-1=2$ since $a^m\times a^n=a^{m+n}$