Originally Posted by

**cristumagnus** Hello. I'm a calculus 1 student in college, and I recently came across a function where x was raised to the (2/3) power. Does anyone in this forum know why a negative number raised to the 2/3 becomes an imaginary number? Type the problem into any calculator, including Google. You'll get an error or an imaginary number.

(-1)^(2/3)

But why does this give you an imaginary number? It's the same as ((-1)^2)^(1/3) or ((-1)^(1/3))^(2). It seems like when you square (-1) you get (1), and the cube root of (-1) is just (-1). Can anyone on this forum explain why this happens?