Question

If $(4^{\sqrt{x}{)}^{\sqrt{x}}}=256$, the value of x is

• A. 2
• B. 4
• C. 16
• D. $\sqrt{2}$

Answer 1

The correct option is B

4

Given, $(4^{\sqrt{x}{)}^{\sqrt{x}}}=256$

$256=4^4$

$\Rightarrow (4^{\sqrt{x}{)}^{\sqrt{x}}}=4^4$

$\because (a^m{)}^n=(a{)}^{m\times n}$

$\Rightarrow (4^{\sqrt{x}\times \sqrt{x}}=4^4$
$\Rightarrow (4{)}^x=4^4$

$\Rightarrow x=4$