SOLUTION: Please help me solve the below algebra problem. The problem should read x to the 3/2 power=125... I tried to set up the problem the best way I could. Thank you :) x^3/2=125

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help me solve the below algebra problem. The problem should read x to the 3/2 power=125... I tried to set up the problem the best way I could. Thank you :) x^3/2=125      Log On


   

Question 578449: Please help me solve the below algebra problem. The problem should read x to the 3/2 power=125... I tried to set up the problem the best way I could. Thank you :)
x^3/2=125
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x^(3/2)=x%5E%283%2F2%29=x%5E1.5=125
The beauty of rational exponents is that they were defined so that the same properties for integer exponents that you knew still hold true. You do not even have to think of the fact that they could be written as roots.
The problem with those fractional exponents is that often I cannot get them to show properly in this website.
I we raise to the exponent 2/3 both sides of that equation, we get
%28x%5E%283%2F2%29%29%5E%282%2F3%29=+125%5E%282%2F3%29 --> x%5E%28%283%2F2%29%282%2F3%29%29=125%5E%282%2F3%29
OK, I mean x^((3/2)(2/3))=125^(2/3)
Of course, %283%2F2%29%282%2F3%29=1, so the equation simplifies to
x^1=125^(2/3) or x=125^(2/3)=root%283%2C125%5E2%29%5E2=%28root%283%2C125%29%29%5E2
That may look complicated, but 125=5%5E3, so
125%5E%282%2F3%29=%285%5E3%29%5E%282%2F3%29=5%5E%283%2A%282%2F3%29%29=5%5E2=25
So highlight%28x=25%29