<s>[INST] Application of AM-GM Inequality 
If $a,b,c >0$ so that $a+b+c=27$ then what is the maximum value of  $(a^2)(b^3)(c^4)$?

I tried the AM-GM inequality but the product term has different powers of $a,b,c$. So how to go about it?
 [/INST] Hint:
$$a+b+c=27 \iff \frac{a}{2}+\frac{a}{2}+\frac{b}{3}+\frac{b}{3}+\frac{b}{3}+\frac{c}{4}+\frac{c}{4}+\frac{c}{4}+\frac{c}{4}=27.$$
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