Algebra Examples

$\frac{m^{\frac{1}{5}} n^{- \frac{1}{7}}}{m^{- \frac{1}{4}} n^{\frac{2}{7}}}$

Step 1

Move $n^{- \frac{1}{7}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{m^{\frac{1}{5}}}{m^{- \frac{1}{4}} n^{\frac{2}{7}} n^{\frac{1}{7}}}$

Step 2

Multiply $n^{\frac{2}{7}}$ by $n^{\frac{1}{7}}$ by adding the exponents.

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Step 2.1

Move $n^{\frac{1}{7}}$ .

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

Step 2.2

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

$\frac{m^{\frac{1}{5}}}{m^{- \frac{1}{4}} n^{\frac{1}{7} + \frac{2}{7}}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{m^{\frac{1}{5}}}{m^{- \frac{1}{4}} n^{\frac{1 + 2}{7}}}$

Step 2.4

Add $1$ and $2$ .

$\frac{m^{\frac{1}{5}}}{m^{- \frac{1}{4}} n^{\frac{3}{7}}}$

Step 3

Move $m^{- \frac{1}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{m^{\frac{1}{5}} m^{\frac{1}{4}}}{n^{\frac{3}{7}}}$

Step 4

Multiply $m^{\frac{1}{5}}$ by $m^{\frac{1}{4}}$ by adding the exponents.

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Step 4.1

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

$\frac{m^{\frac{1}{5} + \frac{1}{4}}}{n^{\frac{3}{7}}}$

Step 4.2

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{m^{\frac{1}{5} \cdot \frac{4}{4} + \frac{1}{4}}}{n^{\frac{3}{7}}}$

Step 4.3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{m^{\frac{1}{5} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{5}{5}}}{n^{\frac{3}{7}}}$

Step 4.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1

Multiply $\frac{1}{5}$ by $\frac{4}{4}$ .

$\frac{m^{\frac{4}{5 \cdot 4} + \frac{1}{4} \cdot \frac{5}{5}}}{n^{\frac{3}{7}}}$

Step 4.4.2

Multiply $5$ by $4$ .

$\frac{m^{\frac{4}{20} + \frac{1}{4} \cdot \frac{5}{5}}}{n^{\frac{3}{7}}}$

Step 4.4.3

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$\frac{m^{\frac{4}{20} + \frac{5}{4 \cdot 5}}}{n^{\frac{3}{7}}}$

Step 4.4.4

Multiply $4$ by $5$ .

$\frac{m^{\frac{4}{20} + \frac{5}{20}}}{n^{\frac{3}{7}}}$

Step 4.5

Combine the numerators over the common denominator.

$\frac{m^{\frac{4 + 5}{20}}}{n^{\frac{3}{7}}}$

Step 4.6

Add $4$ and $5$ .

$\frac{m^{\frac{9}{20}}}{n^{\frac{3}{7}}}$