Answer
$x=\frac{2}{3}$
Work Step by Step
We are given that $64^{x}=16$. Both of these numbers are powers of 4, so we can rewrite the equation as $(4^{3})^{x}=4^{3x}=4^{2}$.
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, $3x=2$.
Divide both sides by 3.
$x=\frac{2}{3}$
