Basic Math Examples

$\frac{35 y}{5} \cdot \frac{y^{8}}{7 y^{6}}$

Step 1

Combine.

$\frac{35 y \cdot y^{8}}{5 (7 y^{6})}$

Step 2

Multiply $y$ by $y^{8}$ by adding the exponents.

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Step 2.1

Move $y^{8}$ .

$\frac{35 (y^{8} y)}{5 (7 y^{6})}$

Step 2.2

Multiply $y^{8}$ by $y$ .

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Step 2.2.1

Raise $y$ to the power of $1$ .

$\frac{35 (y^{8} y^{1})}{5 (7 y^{6})}$

Step 2.2.2

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

$\frac{35 y^{8 + 1}}{5 (7 y^{6})}$

$\frac{35 y^{8 + 1}}{5 (7 y^{6})}$

Step 2.3

Add $8$ and $1$ .

$\frac{35 y^{9}}{5 (7 y^{6})}$

$\frac{35 y^{9}}{5 (7 y^{6})}$

Step 3

Cancel the common factor of $35$ and $5$ .

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Step 3.1

Factor $5$ out of $35 y^{9}$ .

$\frac{5 (7 y^{9})}{5 (7 y^{6})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Cancel the common factor.

$\frac{5 (7 y^{9})}{5 (7 y^{6})}$

Step 3.2.2

Rewrite the expression.

$\frac{7 y^{9}}{7 y^{6}}$

$\frac{7 y^{9}}{7 y^{6}}$

$\frac{7 y^{9}}{7 y^{6}}$

Step 4

Cancel the common factor of $7$ .

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Step 4.1

Cancel the common factor.

$\frac{7 y^{9}}{7 y^{6}}$

Step 4.2

Rewrite the expression.

$\frac{y^{9}}{y^{6}}$

$\frac{y^{9}}{y^{6}}$

Step 5

Cancel the common factor of $y^{9}$ and $y^{6}$ .

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Step 5.1

Factor $y^{6}$ out of $y^{9}$ .

$\frac{y^{6} y^{3}}{y^{6}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

$\frac{y^{6} y^{3}}{y^{6} \cdot 1}$

Step 5.2.2

Cancel the common factor.

$\frac{y^{6} y^{3}}{y^{6} \cdot 1}$

Step 5.2.3

Rewrite the expression.

$\frac{y^{3}}{1}$

Step 5.2.4

Divide $y^{3}$ by $1$ .

$y^{3}$

$y^{3}$

$y^{3}$

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