Algebra Examples

$\frac{3}{48 m^{6} n^{6}} - \frac{7}{8 m^{2} n^{5}}$

Step 1

Cancel the common factor of $3$ and $48$ .

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Step 1.1

Factor $3$ out of $3$ .

$\frac{3 (1)}{48 m^{6} n^{6}} - \frac{7}{8 m^{2} n^{5}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $48 m^{6} n^{6}$ .

$\frac{3 (1)}{3 (16 m^{6} n^{6})} - \frac{7}{8 m^{2} n^{5}}$

Step 1.2.2

Cancel the common factor.

$\frac{3 \cdot 1}{3 (16 m^{6} n^{6})} - \frac{7}{8 m^{2} n^{5}}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{16 m^{6} n^{6}} - \frac{7}{8 m^{2} n^{5}}$

Step 2

To write $- \frac{7}{8 m^{2} n^{5}}$ as a fraction with a common denominator, multiply by $\frac{2 m^{4} n}{2 m^{4} n}$ .

$\frac{1}{16 m^{6} n^{6}} - \frac{7}{8 m^{2} n^{5}} \cdot \frac{2 m^{4} n}{2 m^{4} n}$

Step 3

Write each expression with a common denominator of $16 m^{6} n^{6}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7}{8 m^{2} n^{5}}$ by $\frac{2 m^{4} n}{2 m^{4} n}$ .

$\frac{1}{16 m^{6} n^{6}} - \frac{7 (2 m^{4} n)}{8 m^{2} n^{5} (2 m^{4} n)}$

Step 3.2

Multiply $2$ by $8$ .

$\frac{1}{16 m^{6} n^{6}} - \frac{7 (2 m^{4} n)}{16 m^{2} n^{5} (m^{4} n)}$

Step 3.3

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

$\frac{1}{16 m^{6} n^{6}} - \frac{7 (2 m^{4} n)}{16 m^{4 + 2} n^{5} n}$

Step 3.4

Add $4$ and $2$ .

$\frac{1}{16 m^{6} n^{6}} - \frac{7 (2 m^{4} n)}{16 m^{6} n^{5} n}$

Step 3.5

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

$\frac{1}{16 m^{6} n^{6}} - \frac{7 (2 m^{4} n)}{16 m^{6} (n^{1} n^{5})}$

Step 3.6

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

$\frac{1}{16 m^{6} n^{6}} - \frac{7 (2 m^{4} n)}{16 m^{6} n^{1 + 5}}$

Step 3.7

Add $1$ and $5$ .

$\frac{1}{16 m^{6} n^{6}} - \frac{7 (2 m^{4} n)}{16 m^{6} n^{6}}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 - 7 (2 m^{4} n)}{16 m^{6} n^{6}}$

Step 5

Multiply $- 7$ by $2$ .

$\frac{1 - 14 m^{4} n}{16 m^{6} n^{6}}$