Simplify ((ab^2)^3)/(ab)

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

Simplify the numerator.

Apply the product rule to $a b^{2}$ .

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

Multiply the exponents in ${(b^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $2$ by $3$ .

$\frac{a^{3} b^{6}}{a b}$

Reduce the expression by cancelling the common factors.

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

Factor $a$ out of $a^{3} b^{6}$ .

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

Cancel the common factors.

Factor $a$ out of $a b$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{a^{2} b^{6}}{b}$

Cancel the common factor of $b^{6}$ and $b$ .

Factor $b$ out of $a^{2} b^{6}$ .

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

Cancel the common factors.

Raise $b$ to the power of $1$ .

$\frac{b (a^{2} b^{5})}{b^{1}}$

Factor $b$ out of $b^{1}$ .

$\frac{b (a^{2} b^{5})}{b \cdot 1}$

Cancel the common factor.

$\frac{b (a^{2} b^{5})}{b \cdot 1}$

Rewrite the expression.

$\frac{a^{2} b^{5}}{1}$

Divide $a^{2} b^{5}$ by $1$ .

$a^{2} b^{5}$