Question

If ${\left\{\right(2^4{)}^{1/2}\}}^{?}=256$, find the value of $?$

• A. $1$
• B. $2$
• C. $4$
• D. $8$

Answer 1

Answer: (C)

$4$

Given, ${\left\{\right(2^4{)}^{\frac{1}{2}}\}}^x=256$

${\left\{2^{4\times \frac{1}{2}}\right\}}^x=256$

${\left\{2^2\right\}}^x=256$

${\left\{2^2\right\}}^x=2^8$ (As, 265 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2)

Could be written as

${\left\{2^2\right\}}^x=(2^2{)}^4$

So, $x=4$