Explanation (30 secs solution)

The number of zeros at the end of a number is = Pairs of 2 and 5 in the factors (2*5 = 10)
So lets see the expression
\(x = 3^34^45^56^6-3^64^55^46^3\)
So the first term has \(4^4*6^6\) or \(2^8*2^6*3^6\) or \(2^{14}\) as a factor and \(5^5\). So it has 5 pairs of (2,5). SO the first term has 5 zeros at its end.

Similarly for the second term, \(4^5*6^3\) or \(2^{10}*2^3*3^3\) or \(2^{13}\) as a factor and \(5^4\). So it has 4 pairs of (2,5). SO the second term has 4 zeros at its end.

Therefore x = ....00000- ...0000 = ...0000.

So x has 4 zeros at its end.

please explain the subtraction part in more detail. I dont get this. what is the rule here.

About the subtraction part: If you subtract a number with 4 zeros at the end from a number with 5 zeros at the end will give you a number with 4 zeros.
Lets take this example:

100-10 = 90
1000-100 = 900
10000-1000 = 9000
100000-10000 = 90000

So what you see if I subtract a number with n zeros from a number with (n+1) zeros will result in a number with n zeros at the end.
Please don't hesitate to ask if you don't understand.

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