Simplify (2x^3yz^0)^2

${(2 x^{3} y z^{0})}^{2}$

Anything raised to $0$ is $1$ .

${(2 x^{3} y \cdot 1)}^{2}$

Multiply $2$ by $1$ .

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

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

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

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

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

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

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

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

Multiply the exponents in ${(x^{3})}^{2}$ .

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

$4 x^{3 \cdot 2} y^{2}$

Multiply $3$ by $2$ .

$4 x^{6} y^{2}$