Answer
$x = \dfrac{5}{4}$
Work Step by Step
Rewrite terms so that they both have the same base (note that $4=2^2$ while $32=2^5$):
$$(2^{2})^{2x} = 2^{5}$$
Raising a power to a power means we multiply the exponents (use the rule $\left(a^m\right)^n=a^{mn}$:
$$2^{4x} = 2^{5}$$
If two numbers having the same base are equal, that means that their exponents are also the same, so set the exponents equal to one another to solve for $x$:
$$4x = 5$$
Divide both sides by $4$ to solve for $x$:
$$x = \frac{5}{4}$$
