Simplify ((a^2b)/(b^4))^3

${(\frac{a^{2} b}{b^{4}})}^{3}$

Step 1

Cancel the common factor of $b$ and $b^{4}$ .

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

${(\frac{b a^{2}}{b^{4}})}^{3}$

Cancel the common factors.

Factor $b$ out of $b^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Apply basic rules of exponents.

Apply the product rule to $\frac{a^{2}}{b^{3}}$ .

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

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

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

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

Multiply $2$ by $3$ .

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

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

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

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

Multiply $3$ by $3$ .

$\frac{a^{6}}{b^{9}}$