Simplify ((ab^2)^3)/(b^5)

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

Simplify the numerator.

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

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

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

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

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

Multiply $2$ by $3$ .

$\frac{a^{3} b^{6}}{b^{5}}$

Cancel the common factor of $b^{6}$ and $b^{5}$ .

Factor $b^{5}$ out of $a^{3} b^{6}$ .

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

Cancel the common factors.

Multiply by $1$ .

$\frac{b^{5} (a^{3} b)}{b^{5} \cdot 1}$

Cancel the common factor.

$\frac{b^{5} (a^{3} b)}{b^{5} \cdot 1}$

Rewrite the expression.

$\frac{a^{3} b}{1}$

Divide $a^{3} b$ by $1$ .

$a^{3} b$