Simple Arithmetic

The first step in solving for x is to simplify the right side:

${\displaystyle 2^2{2}^x=2^{2+x}}$

Next, we can re-express the left side as an exponential with 2 as the base.

${\displaystyle 16=2^4}$

Now set the new left side equal to the new right side.

${\displaystyle 2^4=2^{2+x}}$

With the bases now being the same, we can simply set the exponents equal to each other.

${\displaystyle 4=2+x}$

${\displaystyle x=2}$