Question

Solve:

$x=(a^{2/3}{)}^3÷a^{3/2}\times a^{-3}$ If $a=\frac{1}{4}$. Find $x^{-1}$

Answer 1

We have,

$x=(a^{2/3}{)}^3÷a^{3/2}\times a^{-3}$

$\Rightarrow x=a^2÷a^{-3/2}$

$\Rightarrow x=a^2\times a^{3/2}$

$\Rightarrow x=a^{7/2}$

Put $a=\frac{1}{4}$

Therefore,

$\Rightarrow x={\left(\frac{1}{4}\right)}^{7/2}$

$\Rightarrow x={\left(\frac{1}{2}\right)}^7$

$\Rightarrow x=\left(\frac{1}{128}\right)$

$\Rightarrow x^{-1}=128$

Hence, this is the answer.