Question 4028
(x+1)^(-3/2)=8
--------------
Get the cube root of both sides
(x+1)^(-3/2)=8
(x+1)^(-1/2)=2
Square both sides
(x+1)^(-1 = 4
1/(x+1) = 4
4x + 4 = 1
x = -3/4
------------
That's the principal solution.
Do you want the other 2 also?  There are 3 cube roots of 8.