gremather wrote:
Hi, I don't quite understand your last sentence. What do you mean by the limiting number?
amorphous wrote:
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
since for a '\(0\)' to occur \(5\) has to be multiplied by \(2\). The number of zeros will depend on the minimum power raised of either of the two numbers
For eg.
\(100 = 5^2 * 2^2 = 2\) zeros at the end (because both the terms have power raised to 2)
\(125 = 5^3 * 2^0 = 0\) zeros at the end (because 2 is raised to a power of 0 hence 2 becomes the limiting number)