lim x-->0

$\displaystyle \frac{{x}^{x} -1}{x lnx}$

also it says assume as x--> 0 xlnx --> 0

my answer is its 0/0 type since anything to the power of 0 is 1 including $\displaystyle {x}^{x}$ ?

using L H Rule you get

$\displaystyle \frac{{x}^{x} (1+lnx)}{(1+lnx)}$

then again the anything to the power of zero thing gives you that $\displaystyle {x}^{x}$ --> 1