Basic Math Examples

$\frac{256 b^{9}}{a^{12} {(12 a^{2} b)}^{3}}$

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $12 a^{2} b$ .

$\frac{256 b^{9}}{a^{12} {(12 a^{2})}^{3} b^{3}}$

Step 1.2

Apply the product rule to $12 a^{2}$ .

$\frac{256 b^{9}}{a^{12} (12^{3} {(a^{2})}^{3}) b^{3}}$

Step 1.3

Raise $12$ to the power of $3$ .

$\frac{256 b^{9}}{a^{12} (1728 {(a^{2})}^{3}) b^{3}}$

Step 1.4

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

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Step 1.4.1

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

$\frac{256 b^{9}}{a^{12} (1728 a^{2 \cdot 3}) b^{3}}$

Step 1.4.2

Multiply $2$ by $3$ .

$\frac{256 b^{9}}{a^{12} (1728 a^{6}) b^{3}}$

$\frac{256 b^{9}}{a^{12} \cdot 1728 a^{6} b^{3}}$

Step 1.5

Multiply $a^{12}$ by $a^{6}$ by adding the exponents.

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Step 1.5.1

Move $a^{6}$ .

$\frac{256 b^{9}}{a^{6} a^{12} \cdot 1728 b^{3}}$

Step 1.5.2

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

$\frac{256 b^{9}}{a^{6 + 12} \cdot 1728 b^{3}}$

Step 1.5.3

Add $6$ and $12$ .

$\frac{256 b^{9}}{a^{18} \cdot 1728 b^{3}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $256$ and $1728$ .

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Step 2.1.1

Factor $64$ out of $256 b^{9}$ .

$\frac{64 (4 b^{9})}{a^{18} \cdot 1728 b^{3}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $64$ out of $a^{18} \cdot 1728 b^{3}$ .

$\frac{64 (4 b^{9})}{64 (a^{18} \cdot 27 b^{3})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{64 (4 b^{9})}{64 (a^{18} \cdot 27 b^{3})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{4 b^{9}}{a^{18} \cdot 27 b^{3}}$

Step 2.2

Cancel the common factor of $b^{9}$ and $b^{3}$ .

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Step 2.2.1

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

$\frac{b^{3} (4 b^{6})}{a^{18} \cdot 27 b^{3}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $b^{3}$ out of $a^{18} \cdot 27 b^{3}$ .

$\frac{b^{3} (4 b^{6})}{b^{3} (a^{18} \cdot 27)}$

Step 2.2.2.2

Cancel the common factor.

$\frac{b^{3} (4 b^{6})}{b^{3} (a^{18} \cdot 27)}$

Step 2.2.2.3

Rewrite the expression.

$\frac{4 b^{6}}{a^{18} \cdot 27}$

Step 2.3

Move $27$ to the left of $a^{18}$ .

$\frac{4 b^{6}}{27 a^{18}}$