Precalculus Examples

$x^{- \frac{3}{2}} + 2 x^{- \frac{1}{2}} + x^{\frac{1}{2}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{\frac{3}{2}}} + 2 x^{- \frac{1}{2}} + x^{\frac{1}{2}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{\frac{3}{2}}} + 2 \frac{1}{x^{\frac{1}{2}}} + x^{\frac{1}{2}}$

Step 3

Combine $2$ and $\frac{1}{x^{\frac{1}{2}}}$ .

$\frac{1}{x^{\frac{3}{2}}} + \frac{2}{x^{\frac{1}{2}}} + x^{\frac{1}{2}}$

Step 4

Reorder terms.

$x^{\frac{1}{2}} + \frac{1}{x^{\frac{3}{2}}} + \frac{2}{x^{\frac{1}{2}}}$