Precalculus Examples

$\frac{x^{3} y^{- 2} z^{4}}{x^{5} y^{- 2} z^{- 2}}$

Step 1

Move $z^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{x^{3} y^{- 2} z^{4} z^{2}}{x^{5} y^{- 2}}$

Step 2

Multiply $z^{4}$ by $z^{2}$ by adding the exponents.

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Step 2.1

Move $z^{2}$ .

$\frac{x^{3} y^{- 2} (z^{2} z^{4})}{x^{5} y^{- 2}}$

Step 2.2

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

$\frac{x^{3} y^{- 2} z^{2 + 4}}{x^{5} y^{- 2}}$

Step 2.3

Add $2$ and $4$ .

$\frac{x^{3} y^{- 2} z^{6}}{x^{5} y^{- 2}}$

Step 3

Cancel the common factor of $x^{3}$ and $x^{5}$ .

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Step 3.1

Factor $x^{3}$ out of $x^{3} y^{- 2} z^{6}$ .

$\frac{x^{3} (y^{- 2} z^{6})}{x^{5} y^{- 2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x^{3}$ out of $x^{5} y^{- 2}$ .

$\frac{x^{3} (y^{- 2} z^{6})}{x^{3} (x^{2} y^{- 2})}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{3} (y^{- 2} z^{6})}{x^{3} (x^{2} y^{- 2})}$

Step 3.2.3

Rewrite the expression.

$\frac{y^{- 2} z^{6}}{x^{2} y^{- 2}}$

Step 4

Cancel the common factor of $y^{- 2}$ .

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Step 4.1

Cancel the common factor.

$\frac{y^{- 2} z^{6}}{x^{2} y^{- 2}}$

Step 4.2

Rewrite the expression.

$\frac{z^{6}}{x^{2}}$