Simplify (4b^3*3a^4b^2)/(3a^-2b^4)

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

Step 1

Multiply $b^{3}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

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

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

$\frac{4 b^{2 + 3} \cdot (3 a^{4})}{3 a^{- 2} b^{4}}$

Add $2$ and $3$ .

$\frac{4 b^{5} \cdot (3 a^{4})}{3 a^{- 2} b^{4}}$

Step 2

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

$\frac{4 b^{5} \cdot (3 a^{4}) a^{2}}{3 b^{4}}$

Step 3

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

Move $a^{2}$ .

$\frac{4 b^{5} \cdot (3 (a^{2} a^{4}))}{3 b^{4}}$

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

$\frac{4 b^{5} \cdot (3 a^{2 + 4})}{3 b^{4}}$

Add $2$ and $4$ .

$\frac{4 b^{5} \cdot (3 a^{6})}{3 b^{4}}$

Step 4

Cancel the common factor of $b^{5}$ and $b^{4}$ .

Factor $b^{4}$ out of $4 b^{5} \cdot (3 a^{6})$ .

$\frac{b^{4} (4 b \cdot (3 a^{6}))}{3 b^{4}}$

Cancel the common factors.

Factor $b^{4}$ out of $3 b^{4}$ .

$\frac{b^{4} (4 b \cdot (3 a^{6}))}{b^{4} \cdot 3}$

Cancel the common factor.

$\frac{b^{4} (4 b \cdot (3 a^{6}))}{b^{4} \cdot 3}$

Rewrite the expression.

$\frac{4 b \cdot (3 a^{6})}{3}$

Step 5

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{4 b \cdot (3 a^{6})}{3}$

Divide $4 b \cdot (a^{6})$ by $1$ .

$4 b \cdot (a^{6})$

$4 b a^{6}$