Algebra Examples

${(x^{- 2} y^{0} z^{3})}^{- 3}$

Step 1

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

${(\frac{1}{x^{2}} y^{0} z^{3})}^{- 3}$

Step 2

Simplify the expression.

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Step 2.1

Anything raised to $0$ is $1$ .

${(\frac{1}{x^{2}} \cdot 1 z^{3})}^{- 3}$

Step 2.2

Multiply $\frac{1}{x^{2}}$ by $1$ .

${(\frac{1}{x^{2}} z^{3})}^{- 3}$

Step 3

Combine $\frac{1}{x^{2}}$ and $z^{3}$ .

${(\frac{z^{3}}{x^{2}})}^{- 3}$

Step 4

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

${(\frac{x^{2}}{z^{3}})}^{3}$

Step 5

Apply the product rule to $\frac{x^{2}}{z^{3}}$ .

$\frac{{(x^{2})}^{3}}{{(z^{3})}^{3}}$

Step 6

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 6.1

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

$\frac{x^{2 \cdot 3}}{{(z^{3})}^{3}}$

Step 6.2

Multiply $2$ by $3$ .

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Multiply $3$ by $3$ .

$\frac{x^{6}}{z^{9}}$