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

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

Step 1

Simplify the numerator.

Apply the product rule to $- 3 a^{2} b^{4}$ .

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

Apply the product rule to $- 3 a^{2}$ .

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

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

$\frac{9 {(a^{2})}^{2} {(b^{4})}^{2}}{3 {(a^{2} b)}^{3}}$

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

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

$\frac{9 a^{2 \cdot 2} {(b^{4})}^{2}}{3 {(a^{2} b)}^{3}}$

Multiply $2$ by $2$ .

$\frac{9 a^{4} {(b^{4})}^{2}}{3 {(a^{2} b)}^{3}}$

Multiply the exponents in ${(b^{4})}^{2}$ .

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

$\frac{9 a^{4} b^{4 \cdot 2}}{3 {(a^{2} b)}^{3}}$

Multiply $4$ by $2$ .

$\frac{9 a^{4} b^{8}}{3 {(a^{2} b)}^{3}}$

Step 2

Simplify the denominator.

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

$\frac{9 a^{4} b^{8}}{3 {(a^{2})}^{3} b^{3}}$

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

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

$\frac{9 a^{4} b^{8}}{3 a^{2 \cdot 3} b^{3}}$

Multiply $2$ by $3$ .

$\frac{9 a^{4} b^{8}}{3 a^{6} b^{3}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9 a^{4} b^{8}$ .

$\frac{3 (3 a^{4} b^{8})}{3 a^{6} b^{3}}$

Cancel the common factors.

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

$\frac{3 (3 a^{4} b^{8})}{3 (a^{6} b^{3})}$

Cancel the common factor.

$\frac{3 (3 a^{4} b^{8})}{3 (a^{6} b^{3})}$

Rewrite the expression.

$\frac{3 a^{4} b^{8}}{a^{6} b^{3}}$

Cancel the common factor of $a^{4}$ and $a^{6}$ .

Factor $a^{4}$ out of $3 a^{4} b^{8}$ .

$\frac{a^{4} (3 b^{8})}{a^{6} b^{3}}$

Cancel the common factors.

Factor $a^{4}$ out of $a^{6} b^{3}$ .

$\frac{a^{4} (3 b^{8})}{a^{4} (a^{2} b^{3})}$

Cancel the common factor.

$\frac{a^{4} (3 b^{8})}{a^{4} (a^{2} b^{3})}$

Rewrite the expression.

$\frac{3 b^{8}}{a^{2} b^{3}}$

Cancel the common factor of $b^{8}$ and $b^{3}$ .

Factor $b^{3}$ out of $3 b^{8}$ .

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

Cancel the common factors.

Factor $b^{3}$ out of $a^{2} b^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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