Please help me to solve this:

Let x1,...xn be a sample random from pdf

f(x\t)=tx^(t-1) , 0<x<1 , t>0

1) to show that the pdf belongs to the exponential family

2)To find the lower limit of variance of two estimators unbiased to t

3)Find a enough statistics to t and its distribution

4)Suggest a estimator unbiased to t that be from unbiased function and check if it is efficient

Thank you