Simplify (24a^2b^9c^-7)/(36a^3bc^4)

$\frac{24 a^{2} b^{9} c^{- 7}}{36 a^{3} b c^{4}}$

Step 1

Move $c^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{24 a^{2} b^{9}}{36 a^{3} b c^{4} c^{7}}$

Step 2

Multiply $c^{4}$ by $c^{7}$ by adding the exponents.

Move $c^{7}$ .

$\frac{24 a^{2} b^{9}}{36 a^{3} b (c^{7} c^{4})}$

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

$\frac{24 a^{2} b^{9}}{36 a^{3} b c^{7 + 4}}$

Add $7$ and $4$ .

$\frac{24 a^{2} b^{9}}{36 a^{3} b c^{11}}$

Step 3

Cancel the common factor of $24$ and $36$ .

Factor $12$ out of $24 a^{2} b^{9}$ .

$\frac{12 (2 a^{2} b^{9})}{36 a^{3} b c^{11}}$

Cancel the common factors.

Factor $12$ out of $36 a^{3} b c^{11}$ .

$\frac{12 (2 a^{2} b^{9})}{12 (3 a^{3} b c^{11})}$

Cancel the common factor.

$\frac{12 (2 a^{2} b^{9})}{12 (3 a^{3} b c^{11})}$

Rewrite the expression.

$\frac{2 a^{2} b^{9}}{3 a^{3} b c^{11}}$

Step 4

Cancel the common factor of $a^{2}$ and $a^{3}$ .

Factor $a^{2}$ out of $2 a^{2} b^{9}$ .

$\frac{a^{2} (2 b^{9})}{3 a^{3} b c^{11}}$

Cancel the common factors.

Factor $a^{2}$ out of $3 a^{3} b c^{11}$ .

$\frac{a^{2} (2 b^{9})}{a^{2} (3 a b c^{11})}$

Cancel the common factor.

$\frac{a^{2} (2 b^{9})}{a^{2} (3 a b c^{11})}$

Rewrite the expression.

$\frac{2 b^{9}}{3 a b c^{11}}$

Step 5

Cancel the common factor of $b^{9}$ and $b$ .

Factor $b$ out of $2 b^{9}$ .

$\frac{b (2 b^{8})}{3 a b c^{11}}$

Cancel the common factors.

Factor $b$ out of $3 a b c^{11}$ .

$\frac{b (2 b^{8})}{b (3 a c^{11})}$

Cancel the common factor.

$\frac{b (2 b^{8})}{b (3 a c^{11})}$

Rewrite the expression.

$\frac{2 b^{8}}{3 a c^{11}}$