Simplify ((3ab)^3)/(2ab^2(6a)^2)

$\frac{{(3 a b)}^{3}}{2 a b^{2} {(6 a)}^{2}}$

Simplify the numerator.

Apply the product rule to $3 a b$ .

$\frac{{(3 a)}^{3} b^{3}}{2 a b^{2} {(6 a)}^{2}}$

Apply the product rule to $3 a$ .

$\frac{3^{3} a^{3} b^{3}}{2 a b^{2} {(6 a)}^{2}}$

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

$\frac{27 a^{3} b^{3}}{2 a b^{2} {(6 a)}^{2}}$

Simplify the denominator.

Apply the product rule to $6 a$ .

$\frac{27 a^{3} b^{3}}{2 a b^{2} \cdot 6^{2} a^{2}}$

Multiply $a$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$\frac{27 a^{3} b^{3}}{2 (a^{2} a) b^{2} \cdot 6^{2}}$

Multiply $a^{2}$ by $a$ .

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

$\frac{27 a^{3} b^{3}}{2 (a^{2} a^{1}) b^{2} \cdot 6^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{27 a^{3} b^{3}}{2 a^{2 + 1} b^{2} \cdot 6^{2}}$

Add $2$ and $1$ .

$\frac{27 a^{3} b^{3}}{2 a^{3} b^{2} \cdot 6^{2}}$

Raise $6$ to the power of $2$ .

$\frac{27 a^{3} b^{3}}{2 a^{3} b^{2} \cdot 36}$

Multiply $36$ by $2$ .

$\frac{27 a^{3} b^{3}}{72 a^{3} b^{2}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $27$ and $72$ .

Factor $9$ out of $27 a^{3} b^{3}$ .

$\frac{9 (3 a^{3} b^{3})}{72 a^{3} b^{2}}$

Cancel the common factors.

Factor $9$ out of $72 a^{3} b^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $b^{3}$ and $b^{2}$ .

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

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

Cancel the common factors.

Factor $b^{2}$ out of $8 b^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 b}{8}$

Simplify ((3ab)^3)/(2ab^2(6a)^2)

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