Algebra Examples

${(- 3 x^{- 3} y z^{0})}^{- 6}$

Step 1

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

${(- 3 \frac{1}{x^{3}} y z^{0})}^{- 6}$

Step 2

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

${(\frac{- 3}{x^{3}} y z^{0})}^{- 6}$

Step 3

Move the negative in front of the fraction.

${(- \frac{3}{x^{3}} y z^{0})}^{- 6}$

Step 4

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

${(- \frac{y \cdot 3}{x^{3}} z^{0})}^{- 6}$

Step 5

Simplify the expression.

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Step 5.1

Move $3$ to the left of $y$ .

${(- \frac{3 \cdot y}{x^{3}} z^{0})}^{- 6}$

Step 5.2

Anything raised to $0$ is $1$ .

${(- \frac{3 y}{x^{3}} \cdot 1)}^{- 6}$

Step 5.3

Multiply $- 1$ by $1$ .

${(- \frac{3 y}{x^{3}})}^{- 6}$

Step 6

Change the sign of the exponent by rewriting the base as its reciprocal.

${(- \frac{x^{3}}{3 y})}^{6}$

Step 7

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

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Step 7.1

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

${(- 1)}^{6} {(\frac{x^{3}}{3 y})}^{6}$

Step 7.2

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

${(- 1)}^{6} \frac{{(x^{3})}^{6}}{{(3 y)}^{6}}$

Step 7.3

Apply the product rule to $3 y$ .

${(- 1)}^{6} \frac{{(x^{3})}^{6}}{3^{6} y^{6}}$

Step 8

Raise $- 1$ to the power of $6$ .

$1 \frac{{(x^{3})}^{6}}{3^{6} y^{6}}$

Step 9

Multiply $\frac{{(x^{3})}^{6}}{3^{6} y^{6}}$ by $1$ .

$\frac{{(x^{3})}^{6}}{3^{6} y^{6}}$

Step 10

Multiply the exponents in ${(x^{3})}^{6}$ .

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Step 10.1

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

$\frac{x^{3 \cdot 6}}{3^{6} y^{6}}$

Step 10.2

Multiply $3$ by $6$ .

$\frac{x^{18}}{3^{6} y^{6}}$

Step 11

Raise $3$ to the power of $6$ .

$\frac{x^{18}}{729 y^{6}}$