I have got a transformed uniform distribution. The distribution is of the form:

v= u^w
u: uniform [0; 1] distributed variable
w: constant

Respectively in R Code
v= runif(1000)^w
I want to estimate the parameter w by maximum likelihood estimation.

I am therefore interested in:
1. How to construct a ML-estimator for a uniform distribution mathematically.
2. How to programm an estimator for w in R. Any suggestions are welcome, even if using other methods away from maximum liklihood.