 Hello friends, let's discuss the following question. It says, using binomial theorem evaluate the following. We have to evaluate 102 to the power 5. Let us now understand the key idea behind this question. For this we need to know the expansion of a plus b whole to the power n. It is equal to nc0 a to the power n plus nc1 a to the power n minus 1b plus nc2 a to the power n minus 2 into b to the power 2. So on, the last term will be ncn b to the power n. So this knowledge will be the key idea. Let us now move on to the solution. We have to obtain the value of 102 to the power 5. Now 102 can be written as 100 plus 2. So 102 to the power 5 is equal to 100 plus 2 whole to the power 5. Now here n is 5, a is 100 and b is 2. Now 102 to the power 5 is equal to 100 plus 2 whole to the power 5. Now we use the expansion of a plus b whole to the power n. So we have 5c0 100 to the power 5 plus 5c1 100 to the power 5 minus 1 that is 4 into 2 plus 5c2 into 100 to the power 5 minus 2 that is 3 into 2 to the power 2 plus 5c3 into 100 to the power 2 into 2 to the power 3 plus 5c4 into 100 to the power 1 into 2 to the power 4 plus 5c5 into 2 to the power 5. Now this is again equal to, the first term is 5c0 100 to the power 5. Now 5c0 is 1, so the first term is 100 to the power 5 that is 1, 0, 0, 0. We have 10 zeros plus 100 to the power 4 into 2. Now 5c1 is 5 and 100 to the power 4 is 1, 0, 0, 0. We have 8 zeros up to 1 into 2 plus 5c2 is 10. So the third term is 10 into 100 to the power 3 which is 1, 0, 0, 0, 6 zeros up to 1 into 2 to the power 2 which is 4 plus 5c3 is 10 and the fourth term is 5c3 into 100 to the power 2 which is 1, 0, 0, 0 into 2 to the power 3 which is 8 plus 5c4 is 5 so the fifth term is 5 into 100 into 2 to the power 4 which is 16 plus 5c5 is 1 so the last term is 2 to the power 5 which is 32. Again this is equal to 1, 0, 0, 0, 0 10 times plus 10 into this term that is 1, 0, 0, 9 times 0 plus 40 into this term plus 80 into 10,000 which is 8 lakh plus 80 into 100 that is 8,000 plus 32. Taking the sum of these numbers we get it to be equal to 1, 1, 0, 4, 0, 8, 0, 8, 0, 3, 2, hence 102 to the power 5 is equal to 1, 1, 0, 4, 0, 8, 0, 8, 0, 3, 2. This completes the question. Hope you enjoyed this session. Goodbye and take care.