Answer
$x=-\frac{4}{3}$
Work Step by Step
We are given that $2^{3x}=\frac{1}{16}$. Both of these numbers are powers of 2, so we can rewrite the equation as $2^{3x}=2^{-4}$.
We know that $2^{-4}=\frac{1}{2^{4}}=\frac{1}{16}$.
From the uniqueness of $b^{x}$, we know that $b^{x}=b^{y}$ is equivalent to $x=y$ (when $b\gt0$ and $b\ne1$).
Therefore, $3x=-4$. To solve for x, divide both sides by 3.
$x=-\frac{4}{3}$
