Question

How many zeros does the product of 25^5 ×150^4 ×2008 ^3 end with?

Answer 1

13 trailing zeros

Step-by-step explanation:

Our goal is to rewrite the expression such that we have 10 as a factor. Then the power of 10 will give us the number of trailing zeros.

The product can be rewritten as

`(5^2)^5\cdot(2\cdot3\cdot25)^4\cdot(2^3\cdot251)^3`

which can further be rewritten as

`5^(10)\cdot(2^4)(3^4)(5^8)\cdot2^9\cdot251^3`
`\Rightarrow2^(13)\cdot3^4\cdot5^(18)\cdot251^3`
`10^(13)\cdot3^4\cdot5^6\cdot251^3`

We see that by rewriting our expression 10 appears with a power of 13; therefore, the expression has 13 trailing zeros.