Precalculus Examples

$\frac{{(3 x)}^{3} (6 x)}{42 x^{2}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $6$ and $42$ .

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Step 1.1.1

Factor $6$ out of ${(3 x)}^{3} (6 x)$ .

$\frac{6 ({(3 x)}^{3} (x))}{42 x^{2}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $6$ out of $42 x^{2}$ .

$\frac{6 ({(3 x)}^{3} (x))}{6 (7 x^{2})}$

Step 1.1.2.2

Cancel the common factor.

$\frac{6 ({(3 x)}^{3} (x))}{6 (7 x^{2})}$

Step 1.1.2.3

Rewrite the expression.

$\frac{{(3 x)}^{3} (x)}{7 x^{2}}$

$\frac{{(3 x)}^{3} (x)}{7 x^{2}}$

$\frac{{(3 x)}^{3} (x)}{7 x^{2}}$

Step 1.2

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

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Step 1.2.1

Factor $x$ out of ${(3 x)}^{3} (x)$ .

$\frac{x {(3 x)}^{3}}{7 x^{2}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $x$ out of $7 x^{2}$ .

$\frac{x {(3 x)}^{3}}{x (7 x)}$

Step 1.2.2.2

Cancel the common factor.

$\frac{x {(3 x)}^{3}}{x (7 x)}$

Step 1.2.2.3

Rewrite the expression.

$\frac{{(3 x)}^{3}}{7 x}$

$\frac{{(3 x)}^{3}}{7 x}$

$\frac{{(3 x)}^{3}}{7 x}$

$\frac{{(3 x)}^{3}}{7 x}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $3 x$ .

$\frac{3^{3} x^{3}}{7 x}$

Step 2.2

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

$\frac{27 x^{3}}{7 x}$

$\frac{27 x^{3}}{7 x}$

Step 3

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

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Step 3.1

Factor $x$ out of $27 x^{3}$ .

$\frac{x (27 x^{2})}{7 x}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $7 x$ .

$\frac{x (27 x^{2})}{x \cdot 7}$

Step 3.2.2

Cancel the common factor.

$\frac{x (27 x^{2})}{x \cdot 7}$

Step 3.2.3

Rewrite the expression.

$\frac{27 x^{2}}{7}$

$\frac{27 x^{2}}{7}$

$\frac{27 x^{2}}{7}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$