SOLUTION: Trying to solve this equation for x: 9x^(2/3)-4x^(-4/3)=0 Step by step instructions would be great as I don't understand how to get rid of the powers - I know the answer is +/-

Algebra ->  Algebra  -> Exponents-negative-and-fractional -> SOLUTION: Trying to solve this equation for x: 9x^(2/3)-4x^(-4/3)=0 Step by step instructions would be great as I don't understand how to get rid of the powers - I know the answer is +/-       Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 231101: Trying to solve this equation for x: 9x^(2/3)-4x^(-4/3)=0
Step by step instructions would be great as I don't understand how to get rid of the powers - I know the answer is +/- 2/3
Thank you
Answer by ankor@dixie-net.com(12686) About Me  (Show Source):
You can put this solution on YOUR website!
solve this equation for x: 9x%5E%282%2F3%29-4x%5E%28-4%2F3%29=0
:
Add 4x^(-4/3) to both sides
9x%5E%282%2F3%29+=+4x%5E%28-4%2F3%29
:
The reciprocal gets rid of the negative exponent
9x%5E%282%2F3%29 = 4%2F%28x%5E%284%2F3%29%29
:
Cube both sides; gets rid of the (1/3) exponent
729x^2 = 64%2F%28x%5E4%29
:
Find the square root of both sides
27x = 8%2F%28x%5E2%29
;
multiplied both sides by x^2
27x * x^2 = 8
27x^3 = 8
:
Divide both sides by 27
x^3 = 8%2F27
:
Find the cube root of both sides
x = +/-2%2F3; (Both solutions checked out in the original equation)
;
Did this make sense to you?