Finite Math Examples

$\frac{24 x^{- 6} y^{11} z^{5}}{12 x^{2} y^{4} z^{- 3}}$

Step 1

Move $x^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{24 y^{11} z^{5}}{12 x^{2} y^{4} z^{- 3} x^{6}}$

Step 2

Multiply $x^{2}$ by $x^{6}$ by adding the exponents.

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Step 2.1

Move $x^{6}$ .

$\frac{24 y^{11} z^{5}}{12 (x^{6} x^{2}) y^{4} z^{- 3}}$

Step 2.2

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

$\frac{24 y^{11} z^{5}}{12 x^{6 + 2} y^{4} z^{- 3}}$

Step 2.3

Add $6$ and $2$ .

$\frac{24 y^{11} z^{5}}{12 x^{8} y^{4} z^{- 3}}$

Step 3

Move $z^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{24 y^{11} z^{5} z^{3}}{12 x^{8} y^{4}}$

Step 4

Multiply $z^{5}$ by $z^{3}$ by adding the exponents.

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Step 4.1

Move $z^{3}$ .

$\frac{24 y^{11} (z^{3} z^{5})}{12 x^{8} y^{4}}$

Step 4.2

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

$\frac{24 y^{11} z^{3 + 5}}{12 x^{8} y^{4}}$

Step 4.3

Add $3$ and $5$ .

$\frac{24 y^{11} z^{8}}{12 x^{8} y^{4}}$

Step 5

Cancel the common factor of $24$ and $12$ .

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Step 5.1

Factor $12$ out of $24 y^{11} z^{8}$ .

$\frac{12 (2 y^{11} z^{8})}{12 x^{8} y^{4}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $12$ out of $12 x^{8} y^{4}$ .

$\frac{12 (2 y^{11} z^{8})}{12 (x^{8} y^{4})}$

Step 5.2.2

Cancel the common factor.

$\frac{12 (2 y^{11} z^{8})}{12 (x^{8} y^{4})}$

Step 5.2.3

Rewrite the expression.

$\frac{2 y^{11} z^{8}}{x^{8} y^{4}}$

Step 6

Cancel the common factor of $y^{11}$ and $y^{4}$ .

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Step 6.1

Factor $y^{4}$ out of $2 y^{11} z^{8}$ .

$\frac{y^{4} (2 y^{7} z^{8})}{x^{8} y^{4}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y^{4}$ out of $x^{8} y^{4}$ .

$\frac{y^{4} (2 y^{7} z^{8})}{y^{4} x^{8}}$

Step 6.2.2

Cancel the common factor.

$\frac{y^{4} (2 y^{7} z^{8})}{y^{4} x^{8}}$

Step 6.2.3

Rewrite the expression.

$\frac{2 y^{7} z^{8}}{x^{8}}$