Simplify

$\sqrt[4]{81 x^{8} y^{4} z^{16}}$

$=\left(3^{4} \times x^{8} \times y^{4} \times z^{16}\right)^{\frac{1}{4}}$

$=\left(3^{4}\right)^{\frac{1}{4}} \times\left(x^{8}\right)^{\frac{1}{4}} \times\left(y^{4}\right)^{\frac{1}{4}} \times\left(z^{16}\right)^{\frac{1}{4}} \quad\left[(x \times y \times z \times \ldots)^{a}=x^{a} \times y^{a} \times z^{a} \times \ldots\right]$

$=\left(3^{4 \times \frac{1}{4}}\right) \times\left(x^{8 \times \frac{1}{4}}\right) \times\left(y^{4 \times \frac{1}{4}}\right) \times\left(z^{16 \times \frac{1}{4}}\right) \quad\left[\left(x^{a}\right)^{b}=x^{a b}\right]$

$=3 \times x^{2} \times y \times z^{4}$

$=3 x^{2} y z^{4}$