find the 13th term in the expansion of(9x-1/3rootx)^18,x is not equal to 0.

In case of binomial expansion of (a+b)ⁿ, it is written as

ⁿC₀aⁿ+ⁿC₁a^n-1b+......+ⁿC_nbⁿ

So, for the given expression, the 13th term will be ¹⁸C₁₃(9x)¹³/3⁵x^5/2

18!9¹³x¹³/13!5!9²3x^5/2 = (14)(2)(17)(6)(9)¹¹(x)^21/2

=2856(9)¹¹(x)^21/2

 

This is the 13th term