Finite Math Examples

$\frac{9 x^{2}}{{({(18 x)}^{2})}^{3}}$

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $18 x$ .

$\frac{9 x^{2}}{{(18^{2} x^{2})}^{3}}$

Step 1.2

Apply the product rule to $18^{2} x^{2}$ .

$\frac{9 x^{2}}{{(18^{2})}^{3} {(x^{2})}^{3}}$

Step 1.3

Multiply the exponents in ${(18^{2})}^{3}$ .

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Step 1.3.1

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

$\frac{9 x^{2}}{18^{2 \cdot 3} {(x^{2})}^{3}}$

Step 1.3.2

Multiply $2$ by $3$ .

$\frac{9 x^{2}}{18^{6} {(x^{2})}^{3}}$

Step 1.4

Raise $18$ to the power of $6$ .

$\frac{9 x^{2}}{34012224 {(x^{2})}^{3}}$

Step 1.5

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

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Step 1.5.1

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

$\frac{9 x^{2}}{34012224 x^{2 \cdot 3}}$

Step 1.5.2

Multiply $2$ by $3$ .

$\frac{9 x^{2}}{34012224 x^{6}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $9$ and $34012224$ .

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Step 2.1.1

Factor $9$ out of $9 x^{2}$ .

$\frac{9 (x^{2})}{34012224 x^{6}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $9$ out of $34012224 x^{6}$ .

$\frac{9 (x^{2})}{9 (3779136 x^{6})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{9 x^{2}}{9 (3779136 x^{6})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{x^{2}}{3779136 x^{6}}$

Step 2.2

Cancel the common factor of $x^{2}$ and $x^{6}$ .

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Step 2.2.1

Multiply by $1$ .

$\frac{x^{2} \cdot 1}{3779136 x^{6}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $x^{2}$ out of $3779136 x^{6}$ .

$\frac{x^{2} \cdot 1}{x^{2} (3779136 x^{4})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{x^{2} \cdot 1}{x^{2} (3779136 x^{4})}$

Step 2.2.2.3

Rewrite the expression.

$\frac{1}{3779136 x^{4}}$