SOLUTION: How do I solve with a fraction as power? x^3/4 = -8

Question 339871: How do I solve with a fraction as power?
x^3/4 = -8
Found 2 solutions by solver91311, Jk22:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Take the cube root of both sides:

Raise both sides to the fourth power:

Or, if you happen to be a arithmetic masochist,

Raise both sides to the fourth power:

Take the cube root of both sides:

Bear in mind if you try to work this backwards from the solution to get the original problem, you are going to end up with an either/or situation because:

John

My calculator said it, I believe it, that settles it

Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
x^3/4 = -8 | ^4/3 (x^a)^(1/a)=x^(a/a)=x^1=x
x=(-8)^(4/3)=(-2)^4=16 (3root(-8)=-2, indeed, -2*-2*-2=-8)
Verify : 16^(1/4)=+/-2, (+/-2)^3=+/-8.
( ! However on a calculator, x^q, q rational, is not defined for x<0)
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