Precalculus Examples

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

Step 1

Move $u^{\frac{1}{6}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

$u^{\frac{1}{4} \cdot \frac{3}{3} - \frac{1}{6}}$

Step 2.3

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

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

Step 2.4

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

Tap for more steps...

Step 2.4.1

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

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

Step 2.4.2

Multiply $4$ by $3$ .

$u^{\frac{3}{12} - \frac{1}{6} \cdot \frac{2}{2}}$

Step 2.4.3

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

$u^{\frac{3}{12} - \frac{2}{6 \cdot 2}}$

Step 2.4.4

Multiply $6$ by $2$ .

$u^{\frac{3}{12} - \frac{2}{12}}$

Step 2.5

Combine the numerators over the common denominator.

$u^{\frac{3 - 2}{12}}$

Step 2.6

Subtract $2$ from $3$ .

$u^{\frac{1}{12}}$