Algebra Examples

$\frac{- 2 c^{2} d^{10}}{(- 12 c^{3} d^{7}) (18 c^{9} d^{8})}$

Step 1

Expand $(- 12 c^{3} d^{7}) (18 c^{9} d^{8})$ .

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Step 1.1

Remove parentheses.

$\frac{- 2 c^{2} d^{10}}{- 12 c^{3} d^{7} (18 c^{9}) d^{8}}$

Step 1.2

Remove parentheses.

$\frac{- 2 c^{2} d^{10}}{- 12 c^{3} d^{7} \cdot (18 c^{9} d^{8})}$

Step 1.3

Move $d^{7}$ .

$\frac{- 2 c^{2} d^{10}}{- 12 c^{3} \cdot (18 d^{7} c^{9} d^{8})}$

Step 1.4

Move $c^{3}$ .

$\frac{- 2 c^{2} d^{10}}{- 12 \cdot (18 c^{3} d^{7} c^{9} d^{8})}$

Step 1.5

Multiply $- 12$ by $18$ .

$\frac{- 2 c^{2} d^{10}}{- 216 c^{3} d^{7} c^{9} d^{8}}$

Step 2

Turn the denominator into a polynomial.

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Step 2.1

Start expanding.

$(- 12 c^{3} d^{7}) (18 c^{9} d^{8})$

Step 2.2

Remove parentheses.

$- 12 c^{3} d^{7} (18 c^{9}) d^{8}$

Step 2.3

Remove parentheses.

$- 12 c^{3} d^{7} \cdot 18 c^{9} d^{8}$

Step 2.4

Move $d^{7}$ .

$- 12 c^{3} \cdot 18 d^{7} c^{9} d^{8}$

Step 2.5

Move $c^{3}$ .

$- 12 \cdot 18 c^{3} d^{7} c^{9} d^{8}$

Step 2.6

Multiply $- 12$ by $18$ .

$- 216 c^{3} d^{7} c^{9} d^{8}$

Step 2.7

Multiply $c^{3}$ by $c^{9}$ by adding the exponents.

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Step 2.7.1

Move $c^{9}$ .

$- 216 (c^{9} c^{3}) d^{7} d^{8}$

Step 2.7.2

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

$- 216 c^{9 + 3} d^{7} d^{8}$

Step 2.7.3

Add $9$ and $3$ .

$- 216 c^{12} d^{7} d^{8}$

Step 2.8

Multiply $d^{7}$ by $d^{8}$ by adding the exponents.

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Step 2.8.1

Move $d^{8}$ .

$- 216 c^{12} (d^{8} d^{7})$

Step 2.8.2

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

$- 216 c^{12} d^{8 + 7}$

Step 2.8.3

Add $8$ and $7$ .

$- 216 c^{12} d^{15}$

Step 3

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$216 d^{15} c^{12}$

$0 c^{11}$

$0 c^{10}$

$0 c^{9}$

$0 c^{8}$

$0 c^{7}$

$0 c^{6}$

$0 c^{5}$

$0 c^{4}$

$0 c^{3}$

$0 c^{2}$

$0 c$

$0$

$2 d^{10} c^{2}$

$0 c$

$0$

Step 4

The quotient is $0$ .

$0$