Question

What is the value of $x?$
$x^x=2^{2048}$

• A. 512
• B. 1028
• C. 128
• D. 256

Answer 1

The correct option is D 256

The given equation is:
$x^x=2^{2048}$

We are using the identity:
$\left(a^{mn}\right)=(a^m{)}^n$

Let's rewrite the equation as:
$x^x=2^{2\times 1024}$

We are using the identity:
$\left(a^{mn}\right)=(a^m{)}^n$

$x^x=(2^2{)}^{1024}$
$x^x=(4{)}^{1024}$

$x^x=(4{)}^{2\times 512}$
$x^x=(4^2{)}^{512}$
$x^x=(16{)}^{512}$

$x^x=(16{)}^{2\times 256}$
$x^x=({16}^2{)}^{256}$
$x^x=(256{)}^{256}$

Hence, $x=256$.