Simplify (5x^4y^4z^0)^0

${(5 x^{4} y^{4} z^{0})}^{0}$

Anything raised to $0$ is $1$ .

${(5 x^{4} y^{4} \cdot 1)}^{0}$

Multiply $5$ by $1$ .

${(5 x^{4} y^{4})}^{0}$

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

Apply the product rule to $5 x^{4} y^{4}$ .

${(5 x^{4})}^{0} {(y^{4})}^{0}$

Apply the product rule to $5 x^{4}$ .

$5^{0} {(x^{4})}^{0} {(y^{4})}^{0}$

Anything raised to $0$ is $1$ .

$1 {(x^{4})}^{0} {(y^{4})}^{0}$

Multiply ${(x^{4})}^{0}$ by $1$ .

${(x^{4})}^{0} {(y^{4})}^{0}$

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

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

$x^{4 \cdot 0} {(y^{4})}^{0}$

Multiply $4$ by $0$ .

$x^{0} {(y^{4})}^{0}$

Anything raised to $0$ is $1$ .

$1 {(y^{4})}^{0}$

Multiply ${(y^{4})}^{0}$ by $1$ .

${(y^{4})}^{0}$

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

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

$y^{4 \cdot 0}$

Multiply $4$ by $0$ .

$y^{0}$

Anything raised to $0$ is $1$ .

$1$