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

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

Step 1

Anything raised to $0$ is $1$ .

${(5 x^{4} \cdot 1)}^{- 3}$

Step 2

Multiply $5$ by $1$ .

${(5 x^{4})}^{- 3}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(5 x^{4})}^{3}}$

Step 4

Simplify the denominator.

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

$\frac{1}{5^{3} {(x^{4})}^{3}}$

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

$\frac{1}{125 {(x^{4})}^{3}}$

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

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

$\frac{1}{125 x^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{1}{125 x^{12}}$