Explain how this is happening

y=8^(x^(1/x))

When a power is raised to a power, the powers get multiplied. So this should have been equal to y=8^1, or y=8. The graph of this is not even close to y=8; there are imaginary parts, curves etc. when it should just have been a straight line. Please explain.

Thank you.

if you selected just one x, like 4 ... then this is indeed a straight line but I think a lot of the problem is in where you put the brackets :
The second expression actually " means " x ^ ( xth root )
or the xth root of x
try it with several FIXED numbers :
5^(1/5 ) = 1.37
4^(1/4 ) = 1.41
and they are different for t y = 8

if you calculated 8^4^(1/4) you would get a straight line at y = 8
but 8^(4^(1/4) ) = 18.93 ( different brackets )

now if you think of x^(1/x) the x is varying ... so the 8 is being raised to different powers , as the x increases ... hence the changing curve
___________________
Additional mystery ...LOL
plot y = 8^(x^(1/x) on [0,10] and you get a nice smooth curve , maxing out at about 20, and then falling ..
But ... plot it , on say a TI-85 and use a window of ZOOM 4 ( decimal ) which gives a window of x of [-4.7 to 4.7]

NOW look at all the activity from -4.7 to 0 !!! Wow ... what are these ?

Artifacts !!!...
change window to [-4, 4.7 ] and most disappear , except for a few " dots "
Hmmmmmm
these point with the spikes, are places where the xth root of a negative is defined ... so it tries to join the points ... cute !

that isn't quite correct

it is multiplied when it is like this
(8^x)^(1/x)

x^(1/x) does not = 1 (2 ^(1/2) is the squareroot of 2, which isn't 1)
so 8^(x^(1/x)) does not equal 8


to check it out, go type these two equations into
http://www.wolframalpha.com/
(8^x)^(1/x)
8^(x^(1/x))

y=8^(x^(1/x))
is not the same as
y=(8^x)^(1/x) = 8