Question

If $x^{x\sqrt{x}}={\left(x\sqrt{x}\right)}^x$, find the value of $x$.

• A. $\frac{3}{2}$
• B. $\frac{2}{9}$
• C. $\frac{9}{4}$
• D. $\frac{4}{9}$

Answer 1

Answer: (C)

$\frac{9}{4}$

$x^{x^{3/2}}=(x^{3/2}{)}^x$

$\Rightarrow (x{)}^{\frac{3}{2}}=\frac{3x}{2}$

$\Rightarrow x(\sqrt{x}-\frac{3}{2})=0$

$\Rightarrow x=0$ or $\sqrt{x}=\frac{3}{2}$

$\left(0^{\circ }notdefined\right)\Rightarrow x=\frac{9}{4}\Rightarrow \left(C\right)$