Algebra Examples

$\frac{f^{- \frac{1}{4}}}{4 f^{\frac{1}{2}} \cdot f^{- \frac{1}{3}}}$

Step 1

Multiply $f^{\frac{1}{2}}$ by $f^{- \frac{1}{3}}$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $f^{- \frac{1}{3}}$ .

$\frac{f^{- \frac{1}{4}}}{4 (f^{- \frac{1}{3}} f^{\frac{1}{2}})}$

Step 1.2

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

$\frac{f^{- \frac{1}{4}}}{4 f^{- \frac{1}{3} + \frac{1}{2}}}$

Step 1.3

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{f^{- \frac{1}{4}}}{4 f^{- \frac{1}{3} \cdot \frac{2}{2} + \frac{1}{2}}}$

Step 1.4

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{f^{- \frac{1}{4}}}{4 f^{- \frac{1}{3} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{3}{3}}}$

Step 1.5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.5.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{f^{- \frac{1}{4}}}{4 f^{- \frac{2}{3 \cdot 2} + \frac{1}{2} \cdot \frac{3}{3}}}$

Step 1.5.2

Multiply $3$ by $2$ .

$\frac{f^{- \frac{1}{4}}}{4 f^{- \frac{2}{6} + \frac{1}{2} \cdot \frac{3}{3}}}$

Step 1.5.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{f^{- \frac{1}{4}}}{4 f^{- \frac{2}{6} + \frac{3}{2 \cdot 3}}}$

Step 1.5.4

Multiply $2$ by $3$ .

$\frac{f^{- \frac{1}{4}}}{4 f^{- \frac{2}{6} + \frac{3}{6}}}$

Step 1.6

Combine the numerators over the common denominator.

$\frac{f^{- \frac{1}{4}}}{4 f^{\frac{- 2 + 3}{6}}}$

Step 1.7

Add $- 2$ and $3$ .

$\frac{f^{- \frac{1}{4}}}{4 f^{\frac{1}{6}}}$

Step 2

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

$\frac{1}{4 f^{\frac{1}{6}} f^{\frac{1}{4}}}$

Step 3

Multiply $f^{\frac{1}{6}}$ by $f^{\frac{1}{4}}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $f^{\frac{1}{4}}$ .

$\frac{1}{4 (f^{\frac{1}{4}} f^{\frac{1}{6}})}$

Step 3.2

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

$\frac{1}{4 f^{\frac{1}{4} + \frac{1}{6}}}$

Step 3.3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{4 f^{\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6}}}$

Step 3.4

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{4 f^{\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{2}{2}}}$

Step 3.5

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.5.1

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{1}{4 f^{\frac{3}{4 \cdot 3} + \frac{1}{6} \cdot \frac{2}{2}}}$

Step 3.5.2

Multiply $4$ by $3$ .

$\frac{1}{4 f^{\frac{3}{12} + \frac{1}{6} \cdot \frac{2}{2}}}$

Step 3.5.3

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$\frac{1}{4 f^{\frac{3}{12} + \frac{2}{6 \cdot 2}}}$

Step 3.5.4

Multiply $6$ by $2$ .

$\frac{1}{4 f^{\frac{3}{12} + \frac{2}{12}}}$

Step 3.6

Combine the numerators over the common denominator.

$\frac{1}{4 f^{\frac{3 + 2}{12}}}$

Step 3.7

Add $3$ and $2$ .

$\frac{1}{4 f^{\frac{5}{12}}}$