Exponent problem

[susumandrai]

please tell me if the answer to this question is 15. actually the text book tells its 9. i dont know how to do it then.....
question:
When the expression (15^6) x (28^9) x (35^3) is evaluated, it ends with several consecutive zeros. How many?


Thanks

 

[pka]

please tell me if the answer to this question is 15. actually the text book tells its 9. i dont know how to do it then.....
question:
When the expression (15^6) x (28^9) x (35^3) is evaluated, it ends with several consecutive zeros. How many?

Factor!
\(\displaystyle (15)^6\cdot(28)^9\cdot(35)^3=(3^6\cdot 5^6)(2^{18}\cdot 7^9)(5^3\cdot 7^3)\)

Notice that contains a factor \(\displaystyle 2^9\cdot 5^9=10^9\).

So how many trailing zeros will there be?