Basic Math Examples

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

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 ${(3 y)}^{3} (6 y)$ .

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

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

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

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

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

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

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

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

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $3 y$ .

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

Step 2.2

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

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y$ out of $7 y$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

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

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

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