#### Answer

$x=8$

#### Work Step by Step

RECALL:
For any non-negative real number $a$,
$\left(a^{\frac{1}{4}}\right)^4=a$
Raise both sides of the equation to the fourth power then sue the rule above to simplify.
$\left((x+8)^{\frac{1}{4}}\right)^4=\left((2x)^{\frac{1}{4}}\right)^4
\\x+8=2x$
Subtract $x$ on both sides of the equation to obtain:
$8=2x-x$
$8=x$