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.
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?