 Hello and welcome to the session. I am Asha and I am going to help you with the following question that says if a is to the power n plus b raised to the power n upon a raised to the power n minus 1 plus b raised to the power n minus 1 is the arithmetic mean between a and b then find the value of n. Already when that arithmetic mean between a and b a is to the power n plus b raised to the power n upon a raised to the power n minus 1 plus b raised to the power n minus 1 also arithmetic mean of a and b is a plus b upon 2. So, this is equal to a raised to the power n plus b raised to the power n upon a raised to the power n minus 1 plus b raised to the power n minus 1. Now, on cross multiplying we We hit 2 into a raise to the power n plus b raise to the power n is equal to a plus b into a raise to the power n minus 1 plus b raise to the power n minus 1 equal to 2 into a raise to the power n plus 2 into b raise to the power n is equal to a raise to the power n plus a into b raised to the power n minus 1 plus b into a raised to the power n minus 1 plus b raised to the power n or now taking a raised to the power n and b raised to the power n on the left hand side we have 2 a raised to the power n plus 2 times of b raised to the power n minus a raised to the power n minus b raised to the power n is equal to now Now taking p raised to the power n plus b into a raised to the power n minus 1, now this can foreように as a raised to the power n plus b raised to the power n, is equal to a into b raised to the power n minus 1 is equal to a raised to the power n minus 1. Now on rearranging the terms we have a raised to the power n minus b into a raised a-1 is equal to a into b raised to the power n-1-b raised to the power n. Let us take common. So from here taking a raised to the power n-1 common we have a-b and from here taking b raised to the power n-1 common we have again a-b or we can say that a raised to the power n-1-b raised to the power n-1 into a-b is equal to 0. Now since a and b are two different numbers so a is not equal to b this implies a-b is not equal to 0 and so it further implies that a raised to the power n-1-b raised to the power n-1 is equal to 0 or we can say that a raised to the power n-1 is equal to b raised to the power n-1 or a upon b raised to the power n-1 is equal to 1. So this implies n-1 is equal to 0 since the exponent when a number is 0 its value is equal to 1. Since the value is 1 therefore exponent is 0 this implies n is equal to 1. Therefore our answer is value of n is 1. So this completes the solution take care and have a good day.