Finite Math Examples

$\frac{15 c^{8} d^{12}}{27 c^{- 4} d^{- 8}}$

Step 1

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

$\frac{15 c^{8} d^{12} c^{4}}{27 d^{- 8}}$

Step 2

Move $d^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{15 c^{8} d^{12} c^{4} d^{8}}{27}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $c^{8}$ by $c^{4}$ by adding the exponents.

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Step 3.1.1

Move $c^{4}$ .

$\frac{15 (c^{4} c^{8}) d^{12} d^{8}}{27}$

Step 3.1.2

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

$\frac{15 c^{4 + 8} d^{12} d^{8}}{27}$

Step 3.1.3

Add $4$ and $8$ .

$\frac{15 c^{12} d^{12} d^{8}}{27}$

Step 3.2

Multiply $d^{12}$ by $d^{8}$ by adding the exponents.

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Step 3.2.1

Move $d^{8}$ .

$\frac{15 c^{12} (d^{8} d^{12})}{27}$

Step 3.2.2

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

$\frac{15 c^{12} d^{8 + 12}}{27}$

Step 3.2.3

Add $8$ and $12$ .

$\frac{15 c^{12} d^{20}}{27}$

Step 4

Cancel the common factor of $15$ and $27$ .

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Step 4.1

Factor $3$ out of $15 c^{12} d^{20}$ .

$\frac{3 (5 c^{12} d^{20})}{27}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $27$ .

$\frac{3 (5 c^{12} d^{20})}{3 (9)}$

Step 4.2.2

Cancel the common factor.

$\frac{3 (5 c^{12} d^{20})}{3 \cdot 9}$

Step 4.2.3

Rewrite the expression.

$\frac{5 c^{12} d^{20}}{9}$