Answer
$y=\pm 8$
Work Step by Step
We are asked to solve:
$\sqrt[3]{y^4}=16$
$(y^4)^{1/3}=16$
In order to get rid of the exponent ($1/3$), we raise both sides to the third power:
$((y^4)^{1/3})^3=(16)^3$
$y^4=(16)^3$
$y^4=4096$
(Here we used the basic property of exponents $(y^a)^b=y^{ab}$)
Next, to solve for $y$, we raise both sides to the $\frac{1}{4}^{\text{th}}$ power.
$(y^4)^{1/4}=\pm 4096^{1/4}$
$y=\pm 4096^{1/4}$
$y=\sqrt[4]{2096}$
$y=\pm 8$
We test each solution to make sure that it is not extraneous:
$\sqrt[3]{(8)^4}=16$
$\sqrt[3]{(-8)^4}=16$
Both solutions work, thus the answer is: $y=\pm 8$
