explore what happens for 'n' to the power 'n'
using a power button on a calculator, find a value for n so that
n to the power n = 0.6940041897
my intention was for students to find the value n = 0.325 but actually some found another solution as well (between 0.41 and 0.42)
it was a homing in type of activity - also intending to draw attention to peculiar powers
looking at y = x ^ x on a graphical calculator, I seemed to have inadvertently hit a point around the minimum for this rule
then of course there's always the interesting discussion about what 0 to the power 0 is... the curve heads towards y = 1 but then something curious happens to the left of the y-axis...