Basic Math Examples

$\frac{6}{p^{3} p^{3}} - \frac{8}{p^{4} q}$

Step 1

Multiply $p^{3}$ by $p^{3}$ by adding the exponents.

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Step 1.1

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

$\frac{6}{p^{3 + 3}} - \frac{8}{p^{4} q}$

Step 1.2

Add $3$ and $3$ .

$\frac{6}{p^{6}} - \frac{8}{p^{4} q}$

Step 2

To write $\frac{6}{p^{6}}$ as a fraction with a common denominator, multiply by $\frac{q}{q}$ .

$\frac{6}{p^{6}} \cdot \frac{q}{q} - \frac{8}{p^{4} q}$

Step 3

To write $- \frac{8}{p^{4} q}$ as a fraction with a common denominator, multiply by $\frac{p^{2}}{p^{2}}$ .

$\frac{6}{p^{6}} \cdot \frac{q}{q} - \frac{8}{p^{4} q} \cdot \frac{p^{2}}{p^{2}}$

Step 4

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

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Step 4.1

Multiply $\frac{6}{p^{6}}$ by $\frac{q}{q}$ .

$\frac{6 q}{p^{6} q} - \frac{8}{p^{4} q} \cdot \frac{p^{2}}{p^{2}}$

Step 4.2

Multiply $\frac{8}{p^{4} q}$ by $\frac{p^{2}}{p^{2}}$ .

$\frac{6 q}{p^{6} q} - \frac{8 p^{2}}{p^{4} q p^{2}}$

Step 4.3

Multiply $p^{4}$ by $p^{2}$ by adding the exponents.

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Step 4.3.1

Move $p^{2}$ .

$\frac{6 q}{p^{6} q} - \frac{8 p^{2}}{p^{2} p^{4} q}$

Step 4.3.2

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

$\frac{6 q}{p^{6} q} - \frac{8 p^{2}}{p^{2 + 4} q}$

Step 4.3.3

Add $2$ and $4$ .

$\frac{6 q}{p^{6} q} - \frac{8 p^{2}}{p^{6} q}$

Step 5

Combine the numerators over the common denominator.

$\frac{6 q - 8 p^{2}}{p^{6} q}$

Step 6

Factor $2$ out of $6 q - 8 p^{2}$ .

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Step 6.1

Factor $2$ out of $6 q$ .

$\frac{2 (3 q) - 8 p^{2}}{p^{6} q}$

Step 6.2

Factor $2$ out of $- 8 p^{2}$ .

$\frac{2 (3 q) + 2 (- 4 p^{2})}{p^{6} q}$

Step 6.3

Factor $2$ out of $2 (3 q) + 2 (- 4 p^{2})$ .

$\frac{2 (3 q - 4 p^{2})}{p^{6} q}$