Simplify (3x^2yz^4)^2

${(3 x^{2} y z^{4})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $3 x^{2} y z^{4}$ .

${(3 x^{2} y)}^{2} {(z^{4})}^{2}$

Apply the product rule to $3 x^{2} y$ .

${(3 x^{2})}^{2} y^{2} {(z^{4})}^{2}$

Apply the product rule to $3 x^{2}$ .

$3^{2} {(x^{2})}^{2} y^{2} {(z^{4})}^{2}$

Raise $3$ to the power of $2$ .

$9 {(x^{2})}^{2} y^{2} {(z^{4})}^{2}$

Multiply the exponents in ${(x^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$9 x^{2 \cdot 2} y^{2} {(z^{4})}^{2}$

Multiply $2$ by $2$ .

$9 x^{4} y^{2} {(z^{4})}^{2}$

Multiply the exponents in ${(z^{4})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$9 x^{4} y^{2} z^{4 \cdot 2}$

Multiply $4$ by $2$ .

$9 x^{4} y^{2} z^{8}$