Simplify (14a^4b^3-20a^2b^2+2ab)*(2ab)^-1

$(14 a^{4} b^{3} - 20 a^{2} b^{2} + 2 a b) \cdot {(2 a b)}^{- 1}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(14 a^{4} b^{3} - 20 a^{2} b^{2} + 2 a b) \cdot \frac{1}{2 a b}$

Step 2

Multiply $14 a^{4} b^{3} - 20 a^{2} b^{2} + 2 a b$ by $\frac{1}{2 a b}$ .

$\frac{14 a^{4} b^{3} - 20 a^{2} b^{2} + 2 a b}{2 a b}$

Step 3

Factor $2 a b$ out of $14 a^{4} b^{3} - 20 a^{2} b^{2} + 2 a b$ .

Factor $2 a b$ out of $14 a^{4} b^{3}$ .

$\frac{2 a b (7 a^{3} b^{2}) - 20 a^{2} b^{2} + 2 a b}{2 a b}$

Factor $2 a b$ out of $- 20 a^{2} b^{2}$ .

$\frac{2 a b (7 a^{3} b^{2}) + 2 a b (- 10 a b) + 2 a b}{2 a b}$

Factor $2 a b$ out of $2 a b$ .

$\frac{2 a b (7 a^{3} b^{2}) + 2 a b (- 10 a b) + 2 a b (1)}{2 a b}$

Factor $2 a b$ out of $2 a b (7 a^{3} b^{2}) + 2 a b (- 10 a b)$ .

$\frac{2 a b (7 a^{3} b^{2} - 10 a b) + 2 a b (1)}{2 a b}$

Factor $2 a b$ out of $2 a b (7 a^{3} b^{2} - 10 a b) + 2 a b (1)$ .

$\frac{2 a b (7 a^{3} b^{2} - 10 a b + 1)}{2 a b}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a b (7 a^{3} b^{2} - 10 a b + 1)}{2 a b}$

Rewrite the expression.

$\frac{a b (7 a^{3} b^{2} - 10 a b + 1)}{a b}$

Step 5

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a b (7 a^{3} b^{2} - 10 a b + 1)}{a b}$

Rewrite the expression.

$\frac{b (7 a^{3} b^{2} - 10 a b + 1)}{b}$

Step 6

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{b (7 a^{3} b^{2} - 10 a b + 1)}{b}$

Divide $7 a^{3} b^{2} - 10 a b + 1$ by $1$ .

$7 a^{3} b^{2} - 10 a b + 1$