Basic Math Examples

$\frac{5 y^{7}}{3 y^{5}} \div \frac{25 y}{9 y^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 y^{7}}{3 y^{5}} \cdot \frac{9 y^{3}}{25 y}$

Step 2

Combine.

$\frac{5 y^{7} (9 y^{3})}{3 y^{5} (25 y)}$

Step 3

Multiply $y^{7}$ by $y^{3}$ by adding the exponents.

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Step 3.1

Move $y^{3}$ .

$\frac{5 (y^{3} y^{7}) \cdot 9}{3 y^{5} (25 y)}$

Step 3.2

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

$\frac{5 y^{3 + 7} \cdot 9}{3 y^{5} (25 y)}$

Step 3.3

Add $3$ and $7$ .

$\frac{5 y^{10} \cdot 9}{3 y^{5} (25 y)}$

Step 4

Multiply $y^{5}$ by $y$ by adding the exponents.

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Step 4.1

Move $y$ .

$\frac{5 y^{10} \cdot 9}{3 (y \cdot y^{5}) \cdot 25}$

Step 4.2

Multiply $y$ by $y^{5}$ .

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Step 4.2.1

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

$\frac{5 y^{10} \cdot 9}{3 (y^{1} y^{5}) \cdot 25}$

Step 4.2.2

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

$\frac{5 y^{10} \cdot 9}{3 y^{1 + 5} \cdot 25}$

Step 4.3

Add $1$ and $5$ .

$\frac{5 y^{10} \cdot 9}{3 y^{6} \cdot 25}$

Step 5

Cancel the common factor of $5$ and $25$ .

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Step 5.1

Factor $5$ out of $5 y^{10} \cdot 9$ .

$\frac{5 (y^{10} \cdot 9)}{3 y^{6} \cdot 25}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $3 y^{6} \cdot 25$ .

$\frac{5 (y^{10} \cdot 9)}{5 (3 y^{6} \cdot 5)}$

Step 5.2.2

Cancel the common factor.

$\frac{5 (y^{10} \cdot 9)}{5 (3 y^{6} \cdot 5)}$

Step 5.2.3

Rewrite the expression.

$\frac{y^{10} \cdot 9}{3 y^{6} \cdot 5}$

Step 6

Cancel the common factor of $y^{10}$ and $y^{6}$ .

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Step 6.1

Factor $y^{6}$ out of $y^{10} \cdot 9$ .

$\frac{y^{6} (y^{4} \cdot 9)}{3 y^{6} \cdot 5}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y^{6}$ out of $3 y^{6} \cdot 5$ .

$\frac{y^{6} (y^{4} \cdot 9)}{y^{6} (3 \cdot 5)}$

Step 6.2.2

Cancel the common factor.

$\frac{y^{6} (y^{4} \cdot 9)}{y^{6} (3 \cdot 5)}$

Step 6.2.3

Rewrite the expression.

$\frac{y^{4} \cdot 9}{3 \cdot 5}$

Step 7

Cancel the common factor of $9$ and $3$ .

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Step 7.1

Factor $3$ out of $y^{4} \cdot 9$ .

$\frac{3 (y^{4} \cdot 3)}{3 \cdot 5}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $3$ out of $3 \cdot 5$ .

$\frac{3 (y^{4} \cdot 3)}{3 (5)}$

Step 7.2.2

Cancel the common factor.

$\frac{3 (y^{4} \cdot 3)}{3 \cdot 5}$

Step 7.2.3

Rewrite the expression.

$\frac{y^{4} \cdot 3}{5}$

Step 8

Move $3$ to the left of $y^{4}$ .

$\frac{3 y^{4}}{5}$