Basic Math Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Combine.

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

Step 3

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

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Step 3.1

Move $c$ .

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

Step 3.2

Multiply $c$ by $c$ .

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

Step 4

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

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Step 4.1

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

$\frac{c^{2} (5 c^{3} (4 b^{2}))}{6 b^{4} c^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $c^{2}$ out of $6 b^{4} c^{2}$ .

$\frac{c^{2} (5 c^{3} (4 b^{2}))}{c^{2} (6 b^{4})}$

Step 4.2.2

Cancel the common factor.

$\frac{c^{2} (5 c^{3} (4 b^{2}))}{c^{2} (6 b^{4})}$

Step 4.2.3

Rewrite the expression.

$\frac{5 c^{3} (4 b^{2})}{6 b^{4}}$

Step 5

Cancel the common factor of $4$ and $6$ .

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Step 5.1

Factor $2$ out of $5 c^{3} (4 b^{2})$ .

$\frac{2 (5 c^{3} (2 b^{2}))}{6 b^{4}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $6 b^{4}$ .

$\frac{2 (5 c^{3} (2 b^{2}))}{2 (3 b^{4})}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (5 c^{3} (2 b^{2}))}{2 (3 b^{4})}$

Step 5.2.3

Rewrite the expression.

$\frac{5 c^{3} (2 b^{2})}{3 b^{4}}$

Step 6

Cancel the common factor of $b^{2}$ and $b^{4}$ .

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Step 6.1

Factor $b^{2}$ out of $5 c^{3} (2 b^{2})$ .

$\frac{b^{2} (5 c^{3} \cdot (2))}{3 b^{4}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $b^{2}$ out of $3 b^{4}$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

Multiply $2$ by $5$ .

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