Simplify (5^3x^2y^4)^0

${(5^{3} x^{2} y^{4})}^{0}$

Raise $5$ to the power of $3$ .

${(125 x^{2} y^{4})}^{0}$

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

Apply the product rule to $125 x^{2} y^{4}$ .

${(125 x^{2})}^{0} {(y^{4})}^{0}$

Apply the product rule to $125 x^{2}$ .

$125^{0} {(x^{2})}^{0} {(y^{4})}^{0}$

Anything raised to $0$ is $1$ .

$1 {(x^{2})}^{0} {(y^{4})}^{0}$

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

${(x^{2})}^{0} {(y^{4})}^{0}$

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

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

$x^{2 \cdot 0} {(y^{4})}^{0}$

Multiply $2$ 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 $1$ .

$1$