Answer
$x=81$.
Work Step by Step
The given expression is
$\Rightarrow \sqrt[3] {x\sqrt x}=9$
We can write as
$\Rightarrow [x^1x^{\frac{1}{2}}]^{\frac{1}{3}}=9$
$\Rightarrow [x^{1+\frac{1}{2}}]^{\frac{1}{3}}=9$
Simplify.
$\Rightarrow [x^{\frac{3}{2}}]^{\frac{1}{3}}=9$
Use the power rule.
$\Rightarrow x^{\frac{3}{2}\cdot \frac{1}{3} }=9$
Simplify.
$\Rightarrow x^{ \frac{1}{2} }=9$
Square both sides.
$\Rightarrow (x^{ \frac{1}{2} })^{2}=(9)^2$
Use the power rule and simplify.
$\Rightarrow x=81$.
