Finite Math Examples

$\frac{4}{c^{5} \cdot c} - \frac{19}{5}$

Step 1

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

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Step 1.1

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

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Step 1.1.1

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

$\frac{4}{c^{5} \cdot c^{1}} - \frac{19}{5}$

Step 1.1.2

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

$\frac{4}{c^{5 + 1}} - \frac{19}{5}$

Step 1.2

Add $5$ and $1$ .

$\frac{4}{c^{6}} - \frac{19}{5}$

Step 2

To write $\frac{4}{c^{6}}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4}{c^{6}} \cdot \frac{5}{5} - \frac{19}{5}$

Step 3

To write $- \frac{19}{5}$ as a fraction with a common denominator, multiply by $\frac{c^{6}}{c^{6}}$ .

$\frac{4}{c^{6}} \cdot \frac{5}{5} - \frac{19}{5} \cdot \frac{c^{6}}{c^{6}}$

Step 4

Write each expression with a common denominator of $5 c^{6}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{4}{c^{6}}$ by $\frac{5}{5}$ .

$\frac{4 \cdot 5}{c^{6} \cdot 5} - \frac{19}{5} \cdot \frac{c^{6}}{c^{6}}$

Step 4.2

Multiply $\frac{19}{5}$ by $\frac{c^{6}}{c^{6}}$ .

$\frac{4 \cdot 5}{c^{6} \cdot 5} - \frac{19 c^{6}}{5 c^{6}}$

Step 4.3

Reorder the factors of $c^{6} \cdot 5$ .

$\frac{4 \cdot 5}{5 c^{6}} - \frac{19 c^{6}}{5 c^{6}}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 \cdot 5 - 19 c^{6}}{5 c^{6}}$

Step 6

Multiply $4$ by $5$ .

$\frac{20 - 19 c^{6}}{5 c^{6}}$