Answers

  • Brainly User
2014-03-31T20:22:36+05:30
(32)^{32*32}=(35-3)^{1024}

using binomial theorem

(35-3)^{1024}=C_{1024}^{1024}35^{1024}+C_{1}^{1024}35^{1023}3^{1}+...+C_{0}^{1024}3^{1024}

all the terms contain power of 35 which is multiple of 7 as 7x5=35

the last term 

C_{0}^{1024}3^{1024}= \frac{1024!}{1024!}3^{1024}=3^{1024}

so 

(32)^{32*32}=(35-3)^{1024}=35k+3^{1024}=7(5k)+3^{1024}

where k is the integer that includes the other things in expansion
so the remainder is 
3^{1024}


0