realize that for a \(0\) to occur there has to be a multiplication of \(5\) and \(2\)

simplify the 1st term \(3^3 4^4 5^5 6^6\)= \(3^3* (2^2)^4*5^5* (2*3)^6\) = \(3^9* 2^1^4* 5^5\)

Similarly simplify the 2nd term that should come out to be \(3^9* 2^1^3* 5^4\)

Subtracting 2nd term from 1st term:take the common term which is whole of the 2nd term

\(3^9*2^1^3*5^4\)\((10-1)\)

now we have to find out the number of zeros in the common term because non common term is 9

2 and 5 multiply to 10. Here the limiting number is 5 which is equal to 4 hence 4 zeros

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This is my response to the question and may be incorrect. Feel free to rectify any mistakes