Simplify (-2c^2d^10)/((-12c^3d^7)(18c^9d^8))

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

Step 1

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

Move $c^{9}$ .

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

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

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

Add $9$ and $3$ .

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

Step 2

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

Move $d^{8}$ .

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

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

$\frac{- 2 c^{2} d^{10}}{- 12 c^{12} d^{8 + 7} \cdot 18}$

Add $8$ and $7$ .

$\frac{- 2 c^{2} d^{10}}{- 12 c^{12} d^{15} \cdot 18}$

Step 3

Cancel the common factor of $- 2$ and $- 12$ .

Factor $- 2$ out of $- 2 c^{2} d^{10}$ .

$\frac{- 2 (c^{2} d^{10})}{- 12 c^{12} d^{15} \cdot 18}$

Cancel the common factors.

Factor $- 2$ out of $- 12 c^{12} d^{15} \cdot 18$ .

$\frac{- 2 (c^{2} d^{10})}{- 2 (6 c^{12} d^{15} \cdot 18)}$

Cancel the common factor.

$\frac{- 2 (c^{2} d^{10})}{- 2 (6 c^{12} d^{15} \cdot 18)}$

Rewrite the expression.

$\frac{c^{2} d^{10}}{6 c^{12} d^{15} \cdot 18}$

Step 4

Cancel the common factor of $c^{2}$ and $c^{12}$ .

Factor $c^{2}$ out of $c^{2} d^{10}$ .

$\frac{c^{2} (d^{10})}{6 c^{12} d^{15} \cdot 18}$

Cancel the common factors.

Factor $c^{2}$ out of $6 c^{12} d^{15} \cdot 18$ .

$\frac{c^{2} (d^{10})}{c^{2} (6 c^{10} d^{15} \cdot 18)}$

Cancel the common factor.

$\frac{c^{2} d^{10}}{c^{2} (6 c^{10} d^{15} \cdot 18)}$

Rewrite the expression.

$\frac{d^{10}}{6 c^{10} d^{15} \cdot 18}$

Step 5

Cancel the common factor of $d^{10}$ and $d^{15}$ .

Multiply by $1$ .

$\frac{d^{10} \cdot 1}{6 c^{10} d^{15} \cdot 18}$

Cancel the common factors.

Factor $d^{10}$ out of $6 c^{10} d^{15} \cdot 18$ .

$\frac{d^{10} \cdot 1}{d^{10} (6 c^{10} d^{5} \cdot 18)}$

Cancel the common factor.

$\frac{d^{10} \cdot 1}{d^{10} (6 c^{10} d^{5} \cdot 18)}$

Rewrite the expression.

$\frac{1}{6 c^{10} d^{5} \cdot 18}$

Step 6

Multiply $18$ by $6$ .

$\frac{1}{108 c^{10} d^{5}}$

Simplify (-2c^2d^10)/((-12c^3d^7)(18c^9d^8))

Related Questions

Support LCMGCF.com by disabling your adblocker.