# Homework Help: Solving equation with negative exponents

1. Jun 17, 2009

### colts_R_best

1. The problem statement, all variables and given/known data

2x^(-1/3)-9x^(-1/6)= -10

2. Relevant equations

?

3. The attempt at a solution
I have tried to factor out x^(-1/6)
x^(-1/6) (2x-9)= -10
I'm not sure thats even right
I have also converted to fractions
1/2x^(1/3)-1/9x^(1/6)= -10
I'm not sure which route to go or if either is right???

2. Jun 17, 2009

### Staff: Mentor

If you write it this way, can you see what you can do to put the left hand side (LHS) over a common denominator in order to proceed?

$$\frac{2}{x^{1/3}} - \frac{9}{x^{1/6}} = -10$$

3. Jun 17, 2009

### Staff: Mentor

And as a further hint, x1/3 = (x1/6)2, so with the right substitution, your equation is quadratic in form.

4. Jun 18, 2009

### Gregg

Yeah always try to notice when you can turn an equation into a quadratic eg.

$x + x^{-1} + A = 0 \Rightarrow x^2+1+Ax= 0$

$e^x + e^{-x} + A = 0 \Rightarrow (e^{x})^2 +1+ Ae^x = 0$

$\cot(x) + \tan(x) + A = 0 \Rightarrow 1 + \tan^2 x +A\tan x= 0$ etc.

substitutions can be helpful aswell, like substitute e^x for y or something.