Question

Simplify the following expression.

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

Answer 1

We have,

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

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

$\Rightarrow x=a^{\frac{1}{2}}\times a^{-3}$

$\Rightarrow x=a^{-5/2}$

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

Therefore,

$\Rightarrow x={\left(\frac{1}{4}\right)}^{-5/2}$

$\Rightarrow x={\left(\frac{1}{2}\right)}^{-5}$

$\Rightarrow x=\left(32\right)$

$\Rightarrow x^{-1}=\frac{1}{32}$

Hence, this is the answer.