Precalculus Examples

${(\frac{12 x^{- 5} y^{- 3} z^{4}}{3 x y^{- 3} z^{- 4}})}^{- 1}$

Step 1

Move $x^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{12 y^{- 3} z^{4}}{3 x y^{- 3} z^{- 4} x^{5}})}^{- 1}$

Step 2

Multiply $x$ by $x^{5}$ by adding the exponents.

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Step 2.1

Move $x^{5}$ .

${(\frac{12 y^{- 3} z^{4}}{3 (x^{5} x) y^{- 3} z^{- 4}})}^{- 1}$

Step 2.2

Multiply $x^{5}$ by $x$ .

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Step 2.2.1

Raise $x$ to the power of $1$ .

${(\frac{12 y^{- 3} z^{4}}{3 (x^{5} x^{1}) y^{- 3} z^{- 4}})}^{- 1}$

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{12 y^{- 3} z^{4}}{3 x^{5 + 1} y^{- 3} z^{- 4}})}^{- 1}$

Step 2.3

Add $5$ and $1$ .

${(\frac{12 y^{- 3} z^{4}}{3 x^{6} y^{- 3} z^{- 4}})}^{- 1}$

Step 3

Move $z^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{12 y^{- 3} z^{4} z^{4}}{3 x^{6} y^{- 3}})}^{- 1}$

Step 4

Multiply $z^{4}$ by $z^{4}$ by adding the exponents.

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Step 4.1

Move $z^{4}$ .

${(\frac{12 y^{- 3} (z^{4} z^{4})}{3 x^{6} y^{- 3}})}^{- 1}$

Step 4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{12 y^{- 3} z^{4 + 4}}{3 x^{6} y^{- 3}})}^{- 1}$

Step 4.3

Add $4$ and $4$ .

${(\frac{12 y^{- 3} z^{8}}{3 x^{6} y^{- 3}})}^{- 1}$

Step 5

Cancel the common factor of $12$ and $3$ .

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Step 5.1

Factor $3$ out of $12 y^{- 3} z^{8}$ .

${(\frac{3 (4 y^{- 3} z^{8})}{3 x^{6} y^{- 3}})}^{- 1}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $3 x^{6} y^{- 3}$ .

${(\frac{3 (4 y^{- 3} z^{8})}{3 (x^{6} y^{- 3})})}^{- 1}$

Step 5.2.2

Cancel the common factor.

${(\frac{3 (4 y^{- 3} z^{8})}{3 (x^{6} y^{- 3})})}^{- 1}$

Step 5.2.3

Rewrite the expression.

${(\frac{4 y^{- 3} z^{8}}{x^{6} y^{- 3}})}^{- 1}$

Step 6

Cancel the common factor of $y^{- 3}$ .

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Step 6.1

Cancel the common factor.

${(\frac{4 y^{- 3} z^{8}}{x^{6} y^{- 3}})}^{- 1}$

Step 6.2

Rewrite the expression.

${(\frac{4 z^{8}}{x^{6}})}^{- 1}$

Step 7

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

$\frac{x^{6}}{4 z^{8}}$