Answer
$x=-4$
Work Step by Step
The given expression is
$\Rightarrow (\frac{1}{16})^{3x}=64^{2(x+8)}$
Use $16=4^2$ and $64=4^3$.
$\Rightarrow (\frac{1}{4^2})^{3x}=(4^3)^{2(x+8)}$
Use $\frac{1}{a^n}=a^{-n}$.
$\Rightarrow (4^{-2})^{3x}=(4^3)^{2(x+8)}$
Use $(a^n)^m=a^{nm}$.
$\Rightarrow (4)^{-2\cdot 3x}=(4)^{3\cdot 2(x+8)}$
Simplify.
$\Rightarrow (4)^{-6x}=(4)^{6(x+8)}$
Use distributive property.
$\Rightarrow (4)^{-6x}=(4)^{6x+48}$
Equate the exponents.
$\Rightarrow -6x=6x+48$
Add $6x-48$ to each side.
$\Rightarrow -6x+6x-48=6x+48+6x-48$
Simplify.
$\Rightarrow -48=12x$
Divide each side by $12$.
$\Rightarrow -\frac{48}{12}=\frac{12x}{12}$
Simplify.
$\Rightarrow -4=x$
