1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Solving equation with negative exponents

  1. Jun 17, 2009 #1
    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. jcsd
  3. Jun 17, 2009 #2


    User Avatar

    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?

    [tex]\frac{2}{x^{1/3}} - \frac{9}{x^{1/6}} = -10[/tex]
  4. Jun 17, 2009 #3


    Staff: Mentor

    And as a further hint, x1/3 = (x1/6)2, so with the right substitution, your equation is quadratic in form.
  5. Jun 18, 2009 #4
    Yeah always try to notice when you can turn an equation into a quadratic eg.

    [itex] x + x^{-1} + A = 0 \Rightarrow x^2+1+Ax= 0[/itex]

    [itex] e^x + e^{-x} + A = 0 \Rightarrow (e^{x})^2 +1+ Ae^x = 0[/itex]

    [itex] \cot(x) + \tan(x) + A = 0 \Rightarrow 1 + \tan^2 x +A\tan x= 0[/itex] etc.

    substitutions can be helpful aswell, like substitute e^x for y or something.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook