Precalculus Examples

$x^{- \frac{2}{5}} - 3 x^{- \frac{1}{5}} + 1 = 0$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{1}{x^{\frac{2}{5}}} - 3 x^{- \frac{1}{5}} + 1 = 0$

Step 1.2

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

$\frac{1}{x^{\frac{2}{5}}} - 3 \frac{1}{x^{\frac{1}{5}}} + 1 = 0$

Step 1.3

Combine $- 3$ and $\frac{1}{x^{\frac{1}{5}}}$ .

$\frac{1}{x^{\frac{2}{5}}} + \frac{- 3}{x^{\frac{1}{5}}} + 1 = 0$

Step 1.4

Move the negative in front of the fraction.

$\frac{1}{x^{\frac{2}{5}}} - \frac{3}{x^{\frac{1}{5}}} + 1 = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 0.00813061$

Step 3