Pre-Algebra Examples

$\frac{2 a^{4}}{{(3 a^{6} b^{2})}^{3}}$

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $3 a^{6} b^{2}$ .

$\frac{2 a^{4}}{{(3 a^{6})}^{3} {(b^{2})}^{3}}$

Step 1.2

Apply the product rule to $3 a^{6}$ .

$\frac{2 a^{4}}{3^{3} {(a^{6})}^{3} {(b^{2})}^{3}}$

Step 1.3

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

$\frac{2 a^{4}}{27 {(a^{6})}^{3} {(b^{2})}^{3}}$

Step 1.4

Multiply the exponents in ${(a^{6})}^{3}$ .

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Step 1.4.1

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

$\frac{2 a^{4}}{27 a^{6 \cdot 3} {(b^{2})}^{3}}$

Step 1.4.2

Multiply $6$ by $3$ .

$\frac{2 a^{4}}{27 a^{18} {(b^{2})}^{3}}$

Step 1.5

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

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Step 1.5.1

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

$\frac{2 a^{4}}{27 a^{18} b^{2 \cdot 3}}$

Step 1.5.2

Multiply $2$ by $3$ .

$\frac{2 a^{4}}{27 a^{18} b^{6}}$

Step 2

Cancel the common factor of $a^{4}$ and $a^{18}$ .

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Step 2.1

Factor $a^{4}$ out of $2 a^{4}$ .

$\frac{a^{4} \cdot 2}{27 a^{18} b^{6}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $a^{4}$ out of $27 a^{18} b^{6}$ .

$\frac{a^{4} \cdot 2}{a^{4} (27 a^{14} b^{6})}$

Step 2.2.2

Cancel the common factor.

$\frac{a^{4} \cdot 2}{a^{4} (27 a^{14} b^{6})}$

Step 2.2.3

Rewrite the expression.

$\frac{2}{27 a^{14} b^{6}}$