Simplify (-5xy^2z^7)^0

${(- 5 x y^{2} z^{7})}^{0}$

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

Apply the product rule to $- 5 x y^{2} z^{7}$ .

${(- 5 x y^{2})}^{0} {(z^{7})}^{0}$

Apply the product rule to $- 5 x y^{2}$ .

${(- 5 x)}^{0} {(y^{2})}^{0} {(z^{7})}^{0}$

Apply the product rule to $- 5 x$ .

${(- 5)}^{0} x^{0} {(y^{2})}^{0} {(z^{7})}^{0}$

Anything raised to $0$ is $1$ .

$1 x^{0} {(y^{2})}^{0} {(z^{7})}^{0}$

Multiply $x^{0}$ by $1$ .

$x^{0} {(y^{2})}^{0} {(z^{7})}^{0}$

Anything raised to $0$ is $1$ .

$1 {(y^{2})}^{0} {(z^{7})}^{0}$

Multiply ${(y^{2})}^{0}$ by $1$ .

${(y^{2})}^{0} {(z^{7})}^{0}$

Multiply the exponents in ${(y^{2})}^{0}$ .

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

$y^{2 \cdot 0} {(z^{7})}^{0}$

Multiply $2$ by $0$ .

$y^{0} {(z^{7})}^{0}$

Anything raised to $0$ is $1$ .

$1 {(z^{7})}^{0}$

Multiply ${(z^{7})}^{0}$ by $1$ .

${(z^{7})}^{0}$

Multiply the exponents in ${(z^{7})}^{0}$ .

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

$z^{7 \cdot 0}$

Multiply $7$ by $0$ .

$z^{0}$

Anything raised to $0$ is $1$ .

$1$