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

User IClaude
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1 Answer

5 votes

Answer:

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.

User Rocknroll
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