 Hi and welcome to the session. Let us discuss the following question. It says, using binomial theorem, evaluate the following. We have to obtain the value of 101 to the power 4. Now to solve this, we need to know the expansion of A plus B whole to the power n. It is equal to N C 0 A to the power n plus N C 1 A to the power n minus 1 B plus N C 2 A to the power n minus 2 B square. So on, the last term will be N C n B to the power n. So this is the key idea behind this question. Let us now proceed on with the solution. Now 101 can be written as 100 plus 1. So 101 to the power 4 is equal to 100 plus 1 whole to the power 4 and this is in the form A plus B whole to the power n where n is 4, A is 100 and B is 1. Now we expand this using the expansion of A plus B whole to the power n. So 100 plus 1 whole to the power 4 is equal to 4 C 0 100 to the power 4 plus 4 C 1 100 to the power 4 minus 1 that is 3 into B that is 1 plus 4 C 2 into 100 to the power 4 minus 2 that is 2 into 1 to the power 2 plus 4 C 3 into 100 to the power 1 into 1 to the power 3 plus 4 C 4 into 1 to the power 4. Again this is equal to 4 C 0 is 1. So the first term is 100 to the power 4 which is equal to 100 we have 0's 8 times plus 4 C 1 is 4. So the second term is 4 into 100 to the power 3 that is 100 0 0 6 0's after 1 plus 4 C 2 is 6. So the third term is 6 into 100 to the power 2 that is 10000 plus 4 C 3 is 4. So the fourth term is 4 into 100 plus 4 C 4 is 1. So last term is 1 to the power 4 that is 1. Again this is equal to the first term is equal to 100000 8 times plus 4 into this term is 40000 plus 60,000 plus 400 plus 1 and the sum of these numbers is equal to 104060401. Hence 101 to the power 4 is equal to 104060401. So this completes the question. Hope you enjoyed this session. Goodbye and take care.