Basic Math Examples

$\frac{- 8 c d^{5}}{3 c^{4} d^{3}} \cdot \frac{9 c^{3} d^{3}}{6 c d}$

Step 1

Combine.

$\frac{- 8 c d^{5} (9 c^{3} d^{3})}{3 c^{4} d^{3} (6 c d)}$

Step 2

Multiply $c$ by $c^{3}$ by adding the exponents.

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Step 2.1

Move $c^{3}$ .

$\frac{- 8 (c^{3} c) d^{5} (9 d^{3})}{3 c^{4} d^{3} (6 c d)}$

Step 2.2

Multiply $c^{3}$ by $c$ .

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Step 2.2.1

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

$\frac{- 8 (c^{3} c^{1}) d^{5} (9 d^{3})}{3 c^{4} d^{3} (6 c d)}$

Step 2.2.2

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

$\frac{- 8 c^{3 + 1} d^{5} (9 d^{3})}{3 c^{4} d^{3} (6 c d)}$

Step 2.3

Add $3$ and $1$ .

$\frac{- 8 c^{4} d^{5} (9 d^{3})}{3 c^{4} d^{3} (6 c d)}$

Step 3

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

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Step 3.1

Move $d^{3}$ .

$\frac{- 8 c^{4} (d^{3} d^{5}) \cdot 9}{3 c^{4} d^{3} (6 c d)}$

Step 3.2

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

$\frac{- 8 c^{4} d^{3 + 5} \cdot 9}{3 c^{4} d^{3} (6 c d)}$

Step 3.3

Add $3$ and $5$ .

$\frac{- 8 c^{4} d^{8} \cdot 9}{3 c^{4} d^{3} (6 c d)}$

Step 4

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

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Step 4.1

Move $c$ .

$\frac{- 8 c^{4} d^{8} \cdot 9}{3 (c \cdot c^{4}) d^{3} (6 d)}$

Step 4.2

Multiply $c$ by $c^{4}$ .

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Step 4.2.1

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

$\frac{- 8 c^{4} d^{8} \cdot 9}{3 (c^{1} c^{4}) d^{3} (6 d)}$

Step 4.2.2

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

$\frac{- 8 c^{4} d^{8} \cdot 9}{3 c^{1 + 4} d^{3} (6 d)}$

Step 4.3

Add $1$ and $4$ .

$\frac{- 8 c^{4} d^{8} \cdot 9}{3 c^{5} d^{3} (6 d)}$

Step 5

Multiply $d^{3}$ by $d$ by adding the exponents.

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Step 5.1

Move $d$ .

$\frac{- 8 c^{4} d^{8} \cdot 9}{3 c^{5} (d \cdot d^{3}) \cdot 6}$

Step 5.2

Multiply $d$ by $d^{3}$ .

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Step 5.2.1

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

$\frac{- 8 c^{4} d^{8} \cdot 9}{3 c^{5} (d^{1} d^{3}) \cdot 6}$

Step 5.2.2

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

$\frac{- 8 c^{4} d^{8} \cdot 9}{3 c^{5} d^{1 + 3} \cdot 6}$

Step 5.3

Add $1$ and $3$ .

$\frac{- 8 c^{4} d^{8} \cdot 9}{3 c^{5} d^{4} \cdot 6}$

Step 6

Cancel the common factor of $- 8$ and $6$ .

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Step 6.1

Factor $2$ out of $- 8 c^{4} d^{8} \cdot 9$ .

$\frac{2 (- 4 c^{4} d^{8} \cdot 9)}{3 c^{5} d^{4} \cdot 6}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $3 c^{5} d^{4} \cdot 6$ .

$\frac{2 (- 4 c^{4} d^{8} \cdot 9)}{2 (3 c^{5} d^{4} \cdot 3)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (- 4 c^{4} d^{8} \cdot 9)}{2 (3 c^{5} d^{4} \cdot 3)}$

Step 6.2.3

Rewrite the expression.

$\frac{- 4 c^{4} d^{8} \cdot 9}{3 c^{5} d^{4} \cdot 3}$

Step 7

Cancel the common factor of $c^{4}$ and $c^{5}$ .

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Step 7.1

Factor $c^{4}$ out of $- 4 c^{4} d^{8} \cdot 9$ .

$\frac{c^{4} (- 4 d^{8} \cdot 9)}{3 c^{5} d^{4} \cdot 3}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $c^{4}$ out of $3 c^{5} d^{4} \cdot 3$ .

$\frac{c^{4} (- 4 d^{8} \cdot 9)}{c^{4} (3 c d^{4} \cdot 3)}$

Step 7.2.2

Cancel the common factor.

$\frac{c^{4} (- 4 d^{8} \cdot 9)}{c^{4} (3 c d^{4} \cdot 3)}$

Step 7.2.3

Rewrite the expression.

$\frac{- 4 d^{8} \cdot 9}{3 c d^{4} \cdot 3}$

Step 8

Cancel the common factor of $d^{8}$ and $d^{4}$ .

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Step 8.1

Factor $d^{4}$ out of $- 4 d^{8} \cdot 9$ .

$\frac{d^{4} (- 4 d^{4} \cdot 9)}{3 c d^{4} \cdot 3}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $d^{4}$ out of $3 c d^{4} \cdot 3$ .

$\frac{d^{4} (- 4 d^{4} \cdot 9)}{d^{4} (3 c \cdot 3)}$

Step 8.2.2

Cancel the common factor.

$\frac{d^{4} (- 4 d^{4} \cdot 9)}{d^{4} (3 c \cdot 3)}$

Step 8.2.3

Rewrite the expression.

$\frac{- 4 d^{4} \cdot 9}{3 c \cdot 3}$

Step 9

Cancel the common factor of $9$ and $3$ .

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Step 9.1

Factor $3$ out of $- 4 d^{4} \cdot 9$ .

$\frac{3 (- 4 d^{4} \cdot 3)}{3 c \cdot 3}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $3$ out of $3 c \cdot 3$ .

$\frac{3 (- 4 d^{4} \cdot 3)}{3 (c \cdot 3)}$

Step 9.2.2

Cancel the common factor.

$\frac{3 (- 4 d^{4} \cdot 3)}{3 (c \cdot 3)}$

Step 9.2.3

Rewrite the expression.

$\frac{- 4 d^{4} \cdot 3}{c \cdot 3}$

Step 10

Cancel the common factor of $3$ .

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Step 10.1

Cancel the common factor.

$\frac{- 4 d^{4} \cdot 3}{c \cdot 3}$

Step 10.2

Rewrite the expression.

$\frac{- 4 d^{4}}{c}$

Step 11

Move the negative in front of the fraction.

$- \frac{4 d^{4}}{c}$