Basic Math Examples

$\frac{8 c}{6^{2}} \div \frac{4 c^{5}}{5 b^{5} c}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{8 c}{6^{2}} \cdot \frac{5 b^{5} c}{4 c^{5}}$

Step 2

Combine.

$\frac{8 c (5 b^{5} c)}{6^{2} (4 c^{5})}$

Step 3

Multiply $c$ by $c$ by adding the exponents.

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Step 3.1

Move $c$ .

$\frac{8 (c \cdot c) (5 b^{5})}{6^{2} (4 c^{5})}$

Step 3.2

Multiply $c$ by $c$ .

$\frac{8 c^{2} (5 b^{5})}{6^{2} (4 c^{5})}$

Step 4

Cancel the common factor of $8$ and $4$ .

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Step 4.1

Factor $4$ out of $8 c^{2} (5 b^{5})$ .

$\frac{4 (2 c^{2} (5 b^{5}))}{6^{2} (4 c^{5})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $4$ out of $6^{2} (4 c^{5})$ .

$\frac{4 (2 c^{2} (5 b^{5}))}{4 (6^{2} (c^{5}))}$

Step 4.2.2

Cancel the common factor.

$\frac{4 (2 c^{2} (5 b^{5}))}{4 (6^{2} (c^{5}))}$

Step 4.2.3

Rewrite the expression.

$\frac{2 c^{2} (5 b^{5})}{6^{2} (c^{5})}$

Step 5

Cancel the common factor of $c^{2}$ and $c^{5}$ .

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Step 5.1

Factor $c^{2}$ out of $2 c^{2} (5 b^{5})$ .

$\frac{c^{2} (2 (5 b^{5}))}{6^{2} (c^{5})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $c^{2}$ out of $6^{2} (c^{5})$ .

$\frac{c^{2} (2 (5 b^{5}))}{c^{2} (6^{2} (c^{3}))}$

Step 5.2.2

Cancel the common factor.

$\frac{c^{2} (2 (5 b^{5}))}{c^{2} (6^{2} (c^{3}))}$

Step 5.2.3

Rewrite the expression.

$\frac{2 (5 b^{5})}{6^{2} (c^{3})}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $2$ by $5$ .

$\frac{10 b^{5}}{6^{2} c^{3}}$

Step 6.2

Raise $6$ to the power of $2$ .

$\frac{10 b^{5}}{36 c^{3}}$

Step 7

Cancel the common factor of $10$ and $36$ .

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Step 7.1

Factor $2$ out of $10 b^{5}$ .

$\frac{2 (5 b^{5})}{36 c^{3}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $36 c^{3}$ .

$\frac{2 (5 b^{5})}{2 (18 c^{3})}$

Step 7.2.2

Cancel the common factor.

$\frac{2 (5 b^{5})}{2 (18 c^{3})}$

Step 7.2.3

Rewrite the expression.

$\frac{5 b^{5}}{18 c^{3}}$