CAT 2014 Quant - remainders

Was looking for an explanatory solution to the questions below. 1.what is the remainder when 114^210 is divided by 252. What is the remainder when 1532^786 is divided by 253. Last two digits of 1576^689

Was looking for an explanatory solution to the questions below.

1.what is the remainder when 114^210 is divided by 25

2. What is the remainder when 1532^786 is divided by 25

3. Last two digits of 1576^689