Question

determine o valor da potencia:
{[(1/3)²]^6}^7

Answer 1

Utilizando a propriedade:

$\rightarrow~\left(a^b\right)^c=a^{bc}\\\\\\\\\left\{\left[\left(\frac{1}{3}\right)^2 \right]^6 \right\}^7~=~\left\{\left[\frac{1}{3}\right]^{\,2~.~6} \right\}^7~=~\left\{\frac{1}{3} \right\}^{\,2~.~6~.~7}~=~\boxed{\left(\frac{1}{3} \right)^{84}}\\\\\\ou\\\\\left(\frac{1}{3} \right)^{84}~=~\left(\left(3\right)^{-1} \right)^{84}~=~3^{-1~.~84}~=~\boxed{3^{-84}}$