Simplify ((2a^2b)/a)^3

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

Cancel the common factor of $a^{2}$ and $a$ .

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

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

Cancel the common factors.

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

${(\frac{a (2 a b)}{a^{1}})}^{3}$

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

${(\frac{a (2 a b)}{a \cdot 1})}^{3}$

Cancel the common factor.

${(\frac{a (2 a b)}{a \cdot 1})}^{3}$

Rewrite the expression.

${(\frac{2 a b}{1})}^{3}$

Divide $2 a b$ by $1$ .

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $2 a b$ .

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

Apply the product rule to $2 a$ .

$2^{3} a^{3} b^{3}$

Raise $2$ to the power of $3$ .

$8 a^{3} b^{3}$