Simplify (5ab^2-4ab+7a^2b)(ab)^-1

$(5 a b^{2} - 4 a b + 7 a^{2} b) {(a b)}^{- 1}$

Step 1

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

$(5 a b^{2} - 4 a b + 7 a^{2} b) \frac{1}{a b}$

Step 2

Multiply $5 a b^{2} - 4 a b + 7 a^{2} b$ by $\frac{1}{a b}$ .

$\frac{5 a b^{2} - 4 a b + 7 a^{2} b}{a b}$

Step 3

Factor $a b$ out of $5 a b^{2} - 4 a b + 7 a^{2} b$ .

Factor $a b$ out of $5 a b^{2}$ .

$\frac{a b (5 b) - 4 a b + 7 a^{2} b}{a b}$

Factor $a b$ out of $- 4 a b$ .

$\frac{a b (5 b) + a b (- 4) + 7 a^{2} b}{a b}$

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

$\frac{a b (5 b) + a b (- 4) + a b (7 a)}{a b}$

Factor $a b$ out of $a b (5 b) + a b (- 4)$ .

$\frac{a b (5 b - 4) + a b (7 a)}{a b}$

Factor $a b$ out of $a b (5 b - 4) + a b (7 a)$ .

$\frac{a b (5 b - 4 + 7 a)}{a b}$

Step 4

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a b (5 b - 4 + 7 a)}{a b}$

Rewrite the expression.

$\frac{b (5 b - 4 + 7 a)}{b}$

Step 5

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{b (5 b - 4 + 7 a)}{b}$

Divide $5 b - 4 + 7 a$ by $1$ .

$5 b - 4 + 7 a$

Step 6

Simplify the expression.

Move $- 4$ .

$5 b + 7 a - 4$

Reorder $5 b$ and $7 a$ .

$7 a + 5 b - 4$