 Hi, and how are you all today? The question says find the 13th term of the expansion of 9x minus 1 upon 3 under root x, the whole raise to the power 18, where x is not equal to 0. So, we need to find the 13th term. So, what we must know in this question? We must know, first of all, the general term that is t r plus 1 is equal to ncr a raise to the power n minus r b raise to the power r. Right? Now, here we are given the expression that is 9x minus 1 divided by 3 multiplied by under root x, the whole raise to the power 8 provided x is not equal to 0. Now, on comparing here, we have a equal to 9x b equal to minus 1 upon 3 raise to the power x and n equals to 18. Now, substituting a b and the value of n in here and also the value of r that will be, since we are finding the 13th term, r will be equal to 12, isn't it? So, we are finding t 13 that can be written as t 12 plus 1 that is equal to ncr, n is 18 and r is 12. So, we have 18 c 12 a raise to the power a is 9x, a raise to the power n minus r and b raise to the power here b is minus 1 divided by 3 root x to the power 12. Further, on simplifying it, we have 18 factorial divided by 8 factorial multiplied by 12 factorial multiplied by 6 factorial and now 9x raise to the power 6 and minus 1 raise to the power 12, 1 raise to 1 by 3 raise to the power 12 multiplied by 1 by root x raise to the power 12. On simplifying it, we have 18 factorial can be written as 18 into 17 into 16 into 15 into 14 into 13 into 12 factorial divided by 12 factorial, 6 factorial can be written as 6 into 5 into 4 into 3 into 2. Further, we have 9x raise to the power 6 minus 1 raise to the power 12 means 1 itself 1 by 3 raise to the power 12 into here this can be written as 1 by x raise to the power 6. Further, on simplifying we have 4 multiplied by 4 gives us 16. So, here we are left with 6 into 17 into 14 into 13 then we have into 9 raise to the power 6, 1 divided by 1 by 3 raise to the power 12 multiplied by 1 by x raise to the power 6 as well as here we also have x raise to the power 6 in the numerator also. This will become 1 and on simplifying this whole equation we will get 18564. So, the 13th term comes out to be 18564 that is the answer to this question. I hope you enjoyed. Take care of your calculations. Bye for now.