Simplify (-3x^7y^-4z^0)^3

${(- 3 x^{7} y^{- 4} z^{0})}^{3}$

Step 1

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

${(- 3 x^{7} \frac{1}{y^{4}} z^{0})}^{3}$

Step 2

Multiply $- 3 x^{7} \frac{1}{y^{4}}$ .

Combine $- 3$ and $\frac{1}{y^{4}}$ .

${(x^{7} \frac{- 3}{y^{4}} z^{0})}^{3}$

Combine $x^{7}$ and $\frac{- 3}{y^{4}}$ .

${(\frac{x^{7} \cdot - 3}{y^{4}} z^{0})}^{3}$

Step 3

Simplify the expression.

Move $- 3$ to the left of $x^{7}$ .

${(\frac{- 3 \cdot x^{7}}{y^{4}} z^{0})}^{3}$

Move the negative in front of the fraction.

${(- \frac{(3) \cdot x^{7}}{y^{4}} z^{0})}^{3}$

Step 4

Multiply $3$ by $x^{7}$ .

${(- \frac{3 x^{7}}{y^{4}} z^{0})}^{3}$

Step 5

Simplify the expression.

Anything raised to $0$ is $1$ .

${(- \frac{3 x^{7}}{y^{4}} \cdot 1)}^{3}$

Multiply $- 1$ by $1$ .

${(- \frac{3 x^{7}}{y^{4}})}^{3}$

Step 6

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

Apply the product rule to $- \frac{3 x^{7}}{y^{4}}$ .

${(- 1)}^{3} {(\frac{3 x^{7}}{y^{4}})}^{3}$

Apply the product rule to $\frac{3 x^{7}}{y^{4}}$ .

${(- 1)}^{3} \frac{{(3 x^{7})}^{3}}{{(y^{4})}^{3}}$

Apply the product rule to $3 x^{7}$ .

${(- 1)}^{3} \frac{3^{3} {(x^{7})}^{3}}{{(y^{4})}^{3}}$

Step 7

Raise $- 1$ to the power of $3$ .

$- \frac{3^{3} {(x^{7})}^{3}}{{(y^{4})}^{3}}$

Step 8

Simplify the numerator.

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

$- \frac{27 {(x^{7})}^{3}}{{(y^{4})}^{3}}$

Multiply the exponents in ${(x^{7})}^{3}$ .

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

$- \frac{27 x^{7 \cdot 3}}{{(y^{4})}^{3}}$

Multiply $7$ by $3$ .

$- \frac{27 x^{21}}{{(y^{4})}^{3}}$

Step 9

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

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

$- \frac{27 x^{21}}{y^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$- \frac{27 x^{21}}{y^{12}}$

Simplify (-3x^7y^-4z^0)^3

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