 Hello friends, let's discuss the following question. It says, using binomial theorem evaluate the following. We have to obtain the value of 99 to the power 5 and to obtain this value we need to know the expansion of A-B whole to the power n. It is equal to Nc0A to the power n-Nc1A to the power n-1B plus Nc2A to the power n-2B square. So on the last term will be minus 1 to the power n-NcnB to the power n. So this knowledge will work as key idea. Let's now proceed on with the solution. 99 can be written as 100-1. So 99 to the power 5 is equal to 100-1 whole to the power 5. Now this is in the form A-B whole to the power n where n is 5, A is 100 and B is 1. So 99 to the power 5 which is equal to 100-1 whole to the power 5 and this is equal to 5c0100 to the power 5 minus 5c1 100 to the power 5 minus 1 that is 4 into B that is 1 plus 5c2 100 to the power 5 minus 2 that is 3 into 1 to the power 2 minus 5c3 into 100 to the power 2 into 1 to the power 3 plus 5c4 into 100 into 1 to the power 4 plus minus 1 to the power 5 into 5c5 into 1 to the power 5. Now this is equal to 5c0 is 1. So the first term is 100 to the power 5 that is 1 0 0 0 0 0 10 times minus 5c1 100 to the power 4. Now 5c1 is 5 so the second term is 5 into 100 to the power 4 which is 1 0 0 0 0 0 0 plus 5c2 into 100 to the power 3 5c2 is 10. So the third term is 10 into 100 to the power 3 where 100 to the power 3 is 1 0 0 0 0 minus 5c3 is 10 so the fourth term is 10 into 100 to the power 2 and 100 to the power 2 is 1 0 0 0 plus 5c4 is 5 so the fifth term is 5 into 100 and the last term is minus 1 since minus 1 to the power 5 is minus 1 and 5c5 is 1 so the last term is minus 1. Again this is equal to 1 0 0 0 0 0 minus 5 into this term is 5 0 0 0 0 0 8 times plus 10 into this term is 1 0 0 0 0 0 minus 10 into this term is 1 0 0 0 0 plus 500 minus 1 and simplifying this we get it to be equal to 9509900499 hence 99 to the power 5 is equal to 9509900499 so this completes the question hope you enjoyed this session goodbye and take care.