Answer
$x=-\dfrac{2}{3}$
Work Step by Step
$\dfrac{1}{4}=2^{3x}$
Rewrite $4$ as $2^{2}$:
$\dfrac{1}{2^{2}}=2^{3x}$
Take $2^{2}$ to the numerator by changing the sign of its exponent:
$2^{-2}=2^{3x}$
If $2^{-2}=2^{3x}$, then $3x=-2$
$3x=-2$
Solve for $x$:
$x=-\dfrac{2}{3}$