Finite Math Examples

$\frac{x^{\frac{1}{2}}}{x^{\frac{2}{11}}}$

Step 1

Move $x^{\frac{2}{11}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$x^{\frac{1}{2}} x^{- \frac{2}{11}}$

Step 2

Multiply $x^{\frac{1}{2}}$ by $x^{- \frac{2}{11}}$ 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.

$x^{\frac{1}{2} - \frac{2}{11}}$

Step 2.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$x^{\frac{1}{2} \cdot \frac{11}{11} - \frac{2}{11}}$

Step 2.3

To write $- \frac{2}{11}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x^{\frac{1}{2} \cdot \frac{11}{11} - \frac{2}{11} \cdot \frac{2}{2}}$

Step 2.4

Write each expression with a common denominator of $22$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.4.1

Multiply $\frac{1}{2}$ by $\frac{11}{11}$ .

$x^{\frac{11}{2 \cdot 11} - \frac{2}{11} \cdot \frac{2}{2}}$

Step 2.4.2

Multiply $2$ by $11$ .

$x^{\frac{11}{22} - \frac{2}{11} \cdot \frac{2}{2}}$

Step 2.4.3

Multiply $\frac{2}{11}$ by $\frac{2}{2}$ .

$x^{\frac{11}{22} - \frac{2 \cdot 2}{11 \cdot 2}}$

Step 2.4.4

Multiply $11$ by $2$ .

$x^{\frac{11}{22} - \frac{2 \cdot 2}{22}}$

Step 2.5

Combine the numerators over the common denominator.

$x^{\frac{11 - 2 \cdot 2}{22}}$

Step 2.6

Simplify the numerator.

Tap for more steps...

Step 2.6.1

Multiply $- 2$ by $2$ .

$x^{\frac{11 - 4}{22}}$

Step 2.6.2

Subtract $4$ from $11$ .

$x^{\frac{7}{22}}$