I am having trouble getting Maple to work with fractional exponents. When I ask Maple to compute 8^(2/3) and 8^(1/3), it just echoes my input, instead of returning 4 and 2, respectively, as it should (I think the overwhelming majority of mathematicians would agree that Maple should return 4 and 2. It is conventional not to consider complex numbers when defining, e.g., "8^(1/3)" unless a problem specifies that you need to consider complex numbers). When I ask for 4^(1/2), I get 4 inside a square root symbol. This is bizarre, because of course the square root of 4 is 2. When I attempt to plot x^(2/3) from x = -1 to 1, it only plots the positive x part. I can fix this by plotting abs(x)^(2/3), but I'd rather find a way to set some option or something to fix the plot automatically, because I might have to plot something more complicated in the future.
I have attached a worksheet showing what I tried to do.
I have two questions.
How can I get Maple to return the correct, conventional values for these expressions? I would prefer to use fractional exponents rather than "roots" if this is possible.
How can I give Maple some "feedback" about behavior which I consider to be practically a bug (it disagrees with standard mathematical practice)?
EDIT: I'm not sure the upload worked, so I'll cut-and-paste what I can. After 4^(1/2), Maple returned a 4 inside a square root symbol. I couldn't paste both the plots and plot commands here, so here are the plot commands:
8^(2/3);#should be 4
> 8^(1/3);#should be 2
> 4^(1/2);#should be 2
> plot(x^(2/3),x=-1..1);#only plots right part
> plot(abs(x)^(2/3),x=-1..1);#plots what above command should