Simplify ((12a^3b^5)/(4a^6b^3))^3

${(\frac{12 a^{3} b^{5}}{4 a^{6} b^{3}})}^{3}$

Cancel the common factor of $12$ and $4$ .

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Factor $4$ out of $12 a^{3} b^{5}$ .

${(\frac{4 (3 a^{3} b^{5})}{4 a^{6} b^{3}})}^{3}$

Cancel the common factors.

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

${(\frac{4 (3 a^{3} b^{5})}{4 (a^{6} b^{3})})}^{3}$

Cancel the common factor.

${(\frac{4 (3 a^{3} b^{5})}{4 (a^{6} b^{3})})}^{3}$

Rewrite the expression.

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

Cancel the common factor of $a^{3}$ and $a^{6}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $b^{5}$ and $b^{3}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

Simplify the numerator.

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

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

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

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

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

Multiply $2$ by $3$ .

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

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

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

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

Multiply $3$ by $3$ .

$\frac{27 b^{6}}{a^{9}}$

Simplify ((12a^3b^5)/(4a^6b^3))^3

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