Divide (9a^2b^4)/(3a^3b^-3)

$\frac{9 a^{2} b^{4}}{3 a^{3} b^{- 3}}$

Step 1

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

$\frac{9 a^{2} b^{4} b^{3}}{3 a^{3}}$

Step 2

Multiply $b^{4}$ by $b^{3}$ by adding the exponents.

Move $b^{3}$ .

$\frac{9 a^{2} (b^{3} b^{4})}{3 a^{3}}$

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

$\frac{9 a^{2} b^{3 + 4}}{3 a^{3}}$

Add $3$ and $4$ .

$\frac{9 a^{2} b^{7}}{3 a^{3}}$

Step 3

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9 a^{2} b^{7}$ .

$\frac{3 (3 a^{2} b^{7})}{3 a^{3}}$

Cancel the common factors.

Factor $3$ out of $3 a^{3}$ .

$\frac{3 (3 a^{2} b^{7})}{3 (a^{3})}$

Cancel the common factor.

$\frac{3 (3 a^{2} b^{7})}{3 a^{3}}$

Rewrite the expression.

$\frac{3 a^{2} b^{7}}{a^{3}}$

Step 4

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

Factor $a^{2}$ out of $3 a^{2} b^{7}$ .

$\frac{a^{2} (3 b^{7})}{a^{3}}$

Cancel the common factors.

Factor $a^{2}$ out of $a^{3}$ .

$\frac{a^{2} (3 b^{7})}{a^{2} a}$

Cancel the common factor.

$\frac{a^{2} (3 b^{7})}{a^{2} a}$

Rewrite the expression.

$\frac{3 b^{7}}{a}$