Answer
$x=\dfrac{2}{3}$
Work Step by Step
$64^{x}=16$
Since $64=4^{3}$ and $16=4^{2}$, rewrite the equation as $(4^{3})^{x}=4^{2}$:
$(4^{3})^{x}=4^{2}$
Rewrite this equation again, as $4^{3x}=4^{2}$:
$4^{3x}=4^{2}$
If $4^{3x}=4^{2}$, then $3x=2$:
$3x=2$
Solve for $x$ by taking the $3$ to divide the right side:
$x=\dfrac{2}{3}$
