SOLUTION: x^-1.5=27 . . . . . . I know that the answer is 1/9, but I have no idea how to get there.

Algebra ->  Exponents -> SOLUTION: x^-1.5=27 . . . . . . I know that the answer is 1/9, but I have no idea how to get there.      Log On


   

Question 54222: x^-1.5=27 . . . . . . I know that the answer is 1/9, but I have no idea how to get there.
Found 2 solutions by funmath, checkley71:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Another way of saying -1.5 is -3/2. 27=3%5E3 We're going to use these facts to solve the problem.
x%5E-1.5=27
:
x%5E%28-3%2F2%29=3%5E3
:
%28x%5E%28-3%2F2%29%29%5E%28-2%2F3%29=%283%5E3%29%5E%28-2%2F3%29
:
x%5E%286%2F6%29=3%5E%28-6%2F3%29
x=3%5E%28-2%29
x=1%2F%283%5E2%29
highlight%28x=1%2F9%29
Check:
Put this in your calculator:(1/9)^(-1.5) and you'll get 27 and know that you're right!!!!
Happy Calculating!!!

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
X^-1.5=27 OR 1/X^1.5=27 OR SQUARING BOTH SIDES WE GET 1/X^3=27*27 INVERTING BOTH SIDES OF THEEQUATION WE GET X^3=1/27*27 OR X*X*X=1/9*9*9 THEN TAKING THE CUBE ROOT OF BOTH SIDES WE GET X=1/9