(2x-3)^-1/4 = 1/2?

Answer 1

That x is all 'wound up' in that equation is what I tell my students. You want to isolate x by unwinding the equation.

I'm assuming that you meant:

(2x-3)^(-1/4) = 1/2 , you'd better start using more ( ) to avoid ambiguity.

So,
1.
Get rid of that exponent by raising both sides of the equation by -4. Why -4 you say? Because (-1/4)*(-4) = 1. You need to remember your rules for dealing with exponents.

2.
2x-3 = (1/2)^(-4) = 16 , looks better already, doesn't it?
Now, continue to isolate the x by getting rid of that -3 and the 2:

x = (16+3)/2 = 19/2

Answer 2

(2x-3)^-1/4 = 1/2
2x-3 = (1/2)^(-4)
2x-3 = 16
2x = 19

x= 19/2 or 9.5