Question

If $x^{x\sqrt{x}}={\left(x\sqrt{x}\right)}^x$, then x is equal to

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

Answer 1

Answer: (C)

$\frac{9}{4}$

$x^{x\sqrt{x}}=\left(\right(x\sqrt{x}{)}^x)$
$\Rightarrow x^{x\sqrt{x}}={\left(x^{\frac{3}{2}}\right)}^x$
$\Rightarrow x^{x\sqrt{x}}=x^{\frac{3}{2}x}$
$\Rightarrow x\sqrt{x}=\frac{3}{2}x$
$\Rightarrow \sqrt{x}=\frac{3}{2}$
$\Rightarrow x=\frac{9}{4}$