Answer
$x=0,0.5$
Work Step by Step
Re-write the given equation as: $(2^2)^{x^2}=2^{2x^2}$
or, $2^{2x^2}=2^{x}$
Use the rule power rule: $a^p=a^q$ .
We can see that the base $a=2$ is the same on both sides of the equation.
So, the exponents will also be equal.
This implies that $p=q$
Therefore, $ 2x^2=2x \\ 2x^2-x=0 \\ x(2x-1) =0 $
By the zero property rule, we have: $x=0$ and $2x-1=0 \implies x=0.5$
