Simplify (x^3z^0)/((2y^3z^0)^4)

$\frac{x^{3} z^{0}}{{(2 y^{3} z^{0})}^{4}}$

Anything raised to $0$ is $1$ .

$\frac{x^{3} \cdot 1}{{(2 y^{3} z^{0})}^{4}}$

Simplify the denominator.

Apply the product rule to $2 y^{3} z^{0}$ .

$\frac{x^{3} \cdot 1}{{(2 y^{3})}^{4} {(z^{0})}^{4}}$

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

$\frac{x^{3} \cdot 1}{2^{4} {(y^{3})}^{4} {(z^{0})}^{4}}$

Raise $2$ to the power of $4$ .

$\frac{x^{3} \cdot 1}{16 {(y^{3})}^{4} {(z^{0})}^{4}}$

Multiply the exponents in ${(y^{3})}^{4}$ .

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

$\frac{x^{3} \cdot 1}{16 y^{3 \cdot 4} {(z^{0})}^{4}}$

Multiply $3$ by $4$ .

$\frac{x^{3} \cdot 1}{16 y^{12} {(z^{0})}^{4}}$

Multiply the exponents in ${(z^{0})}^{4}$ .

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

$\frac{x^{3} \cdot 1}{16 y^{12} z^{0 \cdot 4}}$

Multiply $0$ by $4$ .

$\frac{x^{3} \cdot 1}{16 y^{12} z^{0}}$

Anything raised to $0$ is $1$ .

$\frac{x^{3} \cdot 1}{16 y^{12} \cdot 1}$

Multiply $16$ by $1$ .

$\frac{x^{3} \cdot 1}{16 y^{12}}$

Multiply $x^{3}$ by $1$ .

$\frac{x^{3}}{16 y^{12}}$