# More problems in 2016

Algebra Level 5

$a^{200} \cdot b^{500} \cdot c^{16} \cdot d^{600} \cdot e^{700}$

Let $$a,b,c,d$$ and $$e$$ be positive reals whose sum is 2016, and $$M$$ the maximum value of the expression above. Then what is the highest power of 3 that divides $$M ?$$

Tip : Wait for the hardest version .

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