<s>[INST] Greatest term in the expansion $(2+3x)^9$ I have got a question which is stated as

Find numerically the greatest term in the expansion of $(2+3x)^9$ where $x=\frac{3}{2}$

I haven't any idea how to proceed but I just plugged in value of $x$ and got $$(2+3x)^9=\bigg(\frac{13}{2}\bigg)^9$$
How can I determine greatest term here?
Please help!!!
 [/INST] You have 
$$(3 x+2)^9=19683 x^9+118098 x^8+314928 x^7+489888 x^6+489888 x^5+326592 x^4+145152 x^3+41472 x^2+6912 x+512$$
Plugging $x=1.5$ the terms, from degree $0$ up are
$$512,10368,93312,489888,1.65337\times 10^6,3.72009\times 10^6,5.58013\times 10^6,5.38084\times 10^6,3.02672\times 10^6,756681$$
the largest terms is  for $x^6$ and is
$5.58013\times 10^6$
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