Pre-Algebra Examples

$\frac{49 c^{5}}{7 c^{4}} \div \frac{{(7 c)}^{3}}{- 42}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{49 c^{5}}{7 c^{4}} \cdot \frac{- 42}{{(7 c)}^{3}}$

Step 2

Combine.

$\frac{49 c^{5} \cdot - 42}{7 c^{4} {(7 c)}^{3}}$

Step 3

Cancel the common factor of $49$ and $7$ .

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Step 3.1

Factor $7$ out of $49 c^{5} \cdot - 42$ .

$\frac{7 (7 c^{5} \cdot - 42)}{7 c^{4} {(7 c)}^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $7$ out of $7 c^{4} {(7 c)}^{3}$ .

$\frac{7 (7 c^{5} \cdot - 42)}{7 (c^{4} {(7 c)}^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{7 (7 c^{5} \cdot - 42)}{7 (c^{4} {(7 c)}^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{7 c^{5} \cdot - 42}{c^{4} {(7 c)}^{3}}$

Step 4

Cancel the common factor of $c^{5}$ and $c^{4}$ .

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Step 4.1

Factor $c^{4}$ out of $7 c^{5} \cdot - 42$ .

$\frac{c^{4} (7 c \cdot - 42)}{c^{4} {(7 c)}^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $c^{4}$ out of $c^{4} {(7 c)}^{3}$ .

$\frac{c^{4} (7 c \cdot - 42)}{c^{4} ({(7 c)}^{3})}$

Step 4.2.2

Cancel the common factor.

$\frac{c^{4} (7 c \cdot - 42)}{c^{4} {(7 c)}^{3}}$

Step 4.2.3

Rewrite the expression.

$\frac{7 c \cdot - 42}{{(7 c)}^{3}}$

Step 5

Multiply $- 42$ by $7$ .

$\frac{- 294 c}{{(7 c)}^{3}}$

Step 6

Simplify the denominator.

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Step 6.1

Apply the product rule to $7 c$ .

$\frac{- 294 c}{7^{3} c^{3}}$

Step 6.2

Raise $7$ to the power of $3$ .

$\frac{- 294 c}{343 c^{3}}$

Step 7

Cancel the common factor of $- 294$ and $343$ .

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Step 7.1

Factor $49$ out of $- 294 c$ .

$\frac{49 (- 6 c)}{343 c^{3}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $49$ out of $343 c^{3}$ .

$\frac{49 (- 6 c)}{49 (7 c^{3})}$

Step 7.2.2

Cancel the common factor.

$\frac{49 (- 6 c)}{49 (7 c^{3})}$

Step 7.2.3

Rewrite the expression.

$\frac{- 6 c}{7 c^{3}}$

Step 8

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

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Step 8.1

Factor $c$ out of $- 6 c$ .

$\frac{c \cdot - 6}{7 c^{3}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $c$ out of $7 c^{3}$ .

$\frac{c \cdot - 6}{c (7 c^{2})}$

Step 8.2.2

Cancel the common factor.

$\frac{c \cdot - 6}{c (7 c^{2})}$

Step 8.2.3

Rewrite the expression.

$\frac{- 6}{7 c^{2}}$

Step 9

Move the negative in front of the fraction.

$- \frac{6}{7 c^{2}}$