Simplify (-28a^6b^-3c^5)/(7a^11b^-5c^5)

$\frac{- 28 a^{6} b^{- 3} c^{5}}{7 a^{11} b^{- 5} c^{5}}$

Step 1

Move $b^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 28 a^{6} b^{- 3} c^{5} b^{5}}{7 a^{11} c^{5}}$

Step 2

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

Move $b^{5}$ .

$\frac{- 28 a^{6} (b^{5} b^{- 3}) c^{5}}{7 a^{11} c^{5}}$

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

$\frac{- 28 a^{6} b^{5 - 3} c^{5}}{7 a^{11} c^{5}}$

Subtract $3$ from $5$ .

$\frac{- 28 a^{6} b^{2} c^{5}}{7 a^{11} c^{5}}$

Step 3

Cancel the common factor of $- 28$ and $7$ .

Factor $7$ out of $- 28 a^{6} b^{2} c^{5}$ .

$\frac{7 (- 4 a^{6} b^{2} c^{5})}{7 a^{11} c^{5}}$

Cancel the common factors.

Factor $7$ out of $7 a^{11} c^{5}$ .

$\frac{7 (- 4 a^{6} b^{2} c^{5})}{7 (a^{11} c^{5})}$

Cancel the common factor.

$\frac{7 (- 4 a^{6} b^{2} c^{5})}{7 (a^{11} c^{5})}$

Rewrite the expression.

$\frac{- 4 a^{6} b^{2} c^{5}}{a^{11} c^{5}}$

Step 4

Cancel the common factor of $a^{6}$ and $a^{11}$ .

Factor $a^{6}$ out of $- 4 a^{6} b^{2} c^{5}$ .

$\frac{a^{6} (- 4 b^{2} c^{5})}{a^{11} c^{5}}$

Cancel the common factors.

Factor $a^{6}$ out of $a^{11} c^{5}$ .

$\frac{a^{6} (- 4 b^{2} c^{5})}{a^{6} (a^{5} c^{5})}$

Cancel the common factor.

$\frac{a^{6} (- 4 b^{2} c^{5})}{a^{6} (a^{5} c^{5})}$

Rewrite the expression.

$\frac{- 4 b^{2} c^{5}}{a^{5} c^{5}}$

Step 5

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

Cancel the common factor.

$\frac{- 4 b^{2} c^{5}}{a^{5} c^{5}}$

Rewrite the expression.

$\frac{- 4 b^{2}}{a^{5}}$

Step 6

Move the negative in front of the fraction.

$- \frac{4 b^{2}}{a^{5}}$