SOLUTION: What is the solution to ((cuberoot 2) raised to the 2 -x) = 2 raised to the x^2

Question 16748: What is the solution to
((cuberoot 2) raised to the 2 -x) = 2 raised to the x^2
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
((cuberoot 2) raised to the 2 -x) = 2 raised to the x^2
note that cube root of x = x^(1/3)...OR IN GENERAL..(x)^(1/p) is called pth. root of x .using this property we get ..
[(2)^(1/3)]^(2-x) = (2)^(x^2)
[(2)^{(2-x)/3}] = (2)^(x^2)..bases being same (2) in this equation,powers should be equal . hence
(2-x)/3 = x^2
2-x = 3x^2
3x^2 + x - 2 = 0
3x^2 +3x - 2x-2 = 0
3x(x+1)-2(x+1) = 0
(x+1)(3x-2)=0
x=-1 or x=2/3
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