Simplify (-12c^3d^0f^-2)/(6c^5d^-3f^4)

$\frac{- 12 c^{3} d^{0} f^{- 2}}{6 c^{5} d^{- 3} f^{4}}$

Step 1

Move $f^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 12 c^{3}}{6 c^{5} d^{- 3} f^{4} f^{2}}$

Step 2

Multiply $f^{4}$ by $f^{2}$ by adding the exponents.

Move $f^{2}$ .

$\frac{- 12 c^{3}}{6 c^{5} d^{- 3} (f^{2} f^{4})}$

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

$\frac{- 12 c^{3}}{6 c^{5} d^{- 3} f^{2 + 4}}$

Add $2$ and $4$ .

$\frac{- 12 c^{3}}{6 c^{5} d^{- 3} f^{6}}$

Step 3

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

$\frac{- 12 c^{3} d^{3}}{6 c^{5} f^{6}}$

Step 4

Cancel the common factor of $- 12$ and $6$ .

Factor $6$ out of $- 12 c^{3} d^{3}$ .

$\frac{6 (- 2 c^{3} d^{3})}{6 c^{5} f^{6}}$

Cancel the common factors.

Factor $6$ out of $6 c^{5} f^{6}$ .

$\frac{6 (- 2 c^{3} d^{3})}{6 (c^{5} f^{6})}$

Cancel the common factor.

$\frac{6 (- 2 c^{3} d^{3})}{6 (c^{5} f^{6})}$

Rewrite the expression.

$\frac{- 2 c^{3} d^{3}}{c^{5} f^{6}}$

Step 5

Cancel the common factor of $c^{3}$ and $c^{5}$ .

Factor $c^{3}$ out of $- 2 c^{3} d^{3}$ .

$\frac{c^{3} (- 2 d^{3})}{c^{5} f^{6}}$

Cancel the common factors.

Factor $c^{3}$ out of $c^{5} f^{6}$ .

$\frac{c^{3} (- 2 d^{3})}{c^{3} (c^{2} f^{6})}$

Cancel the common factor.

$\frac{c^{3} (- 2 d^{3})}{c^{3} (c^{2} f^{6})}$

Rewrite the expression.

$\frac{- 2 d^{3}}{c^{2} f^{6}}$

Step 6

Move the negative in front of the fraction.

$- \frac{2 d^{3}}{c^{2} f^{6}}$