Simplify (12a^-9b^-4)/(9a^2b^6)

$\frac{12 a^{- 9} b^{- 4}}{9 a^{2} b^{6}}$

Step 1

Move $a^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{12 b^{- 4}}{9 a^{2} b^{6} a^{9}}$

Step 2

Move $b^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{12}{9 a^{2} b^{6} a^{9} b^{4}}$

Step 3

Simplify the denominator.

Multiply $a^{2}$ by $a^{9}$ by adding the exponents.

Move $a^{9}$ .

$\frac{12}{9 (a^{9} a^{2}) b^{6} b^{4}}$

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

$\frac{12}{9 a^{9 + 2} b^{6} b^{4}}$

Add $9$ and $2$ .

$\frac{12}{9 a^{11} b^{6} b^{4}}$

Multiply $b^{6}$ by $b^{4}$ by adding the exponents.

Move $b^{4}$ .

$\frac{12}{9 a^{11} (b^{4} b^{6})}$

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

$\frac{12}{9 a^{11} b^{4 + 6}}$

Add $4$ and $6$ .

$\frac{12}{9 a^{11} b^{10}}$

Step 4

Cancel the common factor of $12$ and $9$ .

Factor $3$ out of $12$ .

$\frac{3 (4)}{9 a^{11} b^{10}}$

Cancel the common factors.

Factor $3$ out of $9 a^{11} b^{10}$ .

$\frac{3 (4)}{3 (3 a^{11} b^{10})}$

Cancel the common factor.

$\frac{3 \cdot 4}{3 (3 a^{11} b^{10})}$

Rewrite the expression.

$\frac{4}{3 a^{11} b^{10}}$