Pre-Algebra Examples

$\frac{25 c^{4}}{5 c^{5}} \div \frac{{(5)}^{3}}{- 30}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{25 c^{4}}{5 c^{5}} \cdot \frac{- 30}{{(5)}^{3}}$

Step 2

Combine.

$\frac{25 c^{4} \cdot - 30}{5 c^{5} {(5)}^{3}}$

Step 3

Multiply $5$ by ${(5)}^{3}$ by adding the exponents.

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Step 3.1

Move ${(5)}^{3}$ .

$\frac{25 c^{4} \cdot - 30}{{(5)}^{3} \cdot 5 c^{5}}$

Step 3.2

Multiply ${(5)}^{3}$ by $5$ .

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Step 3.2.1

Raise $5$ to the power of $1$ .

$\frac{25 c^{4} \cdot - 30}{{(5)}^{3} \cdot 5^{1} c^{5}}$

Step 3.2.2

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

$\frac{25 c^{4} \cdot - 30}{5^{3 + 1} c^{5}}$

Step 3.3

Add $3$ and $1$ .

$\frac{25 c^{4} \cdot - 30}{5^{4} c^{5}}$

Step 4

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

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Step 4.1

Factor $c^{4}$ out of $25 c^{4} \cdot - 30$ .

$\frac{c^{4} (25 \cdot - 30)}{5^{4} c^{5}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $c^{4}$ out of $5^{4} c^{5}$ .

$\frac{c^{4} (25 \cdot - 30)}{c^{4} (5^{4} c)}$

Step 4.2.2

Cancel the common factor.

$\frac{c^{4} (25 \cdot - 30)}{c^{4} (5^{4} c)}$

Step 4.2.3

Rewrite the expression.

$\frac{25 \cdot - 30}{5^{4} c}$

Step 5

Multiply $25$ by $- 30$ .

$\frac{- 750}{5^{4} c}$

Step 6

Raise $5$ to the power of $4$ .

$\frac{- 750}{625 c}$

Step 7

Cancel the common factor of $- 750$ and $625$ .

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Step 7.1

Factor $125$ out of $- 750$ .

$\frac{125 (- 6)}{625 c}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $125$ out of $625 c$ .

$\frac{125 (- 6)}{125 (5 c)}$

Step 7.2.2

Cancel the common factor.

$\frac{125 \cdot - 6}{125 (5 c)}$

Step 7.2.3

Rewrite the expression.

$\frac{- 6}{5 c}$

Step 8

Move the negative in front of the fraction.

$- \frac{6}{5 c}$