Answer :

Answer:

13 trailing zeros

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

[tex](5^2)^5\cdot(2\cdot3\cdot25)^4\cdot(2^3\cdot251)^3[/tex]

which can further be rewritten as

[tex]5^{10}\cdot(2^4)(3^4)(5^8)\cdot2^9\cdot251^3[/tex][tex]\Rightarrow2^{13}\cdot3^4\cdot5^{18}\cdot251^3[/tex][tex]10^{13}\cdot3^4\cdot5^6\cdot251^3[/tex]

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

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