How many zeros

[kory]

I have to find the number of zeros in 45^7 * 88^5 without computing.
The problem also mentions that 45^7 * 88^5 has 15 factors of 2. How is there 15 factors of 2??? I dont understand where 15 comes from.

 

[Deleted member 4993]

I have to find the number of zeros in 45^7 * 88^5 without computing.
The problem also mentions that 45^7 * 88^5 has 15 factors of 2. How is there 15 factors of 2??? I dont understand where 15 comes from.

88 = 2³ * 11

88^5 = (2³ * 11)⁵

There... now continue....

 

[lev888]

I have to find the number of zeros in 45^7 * 88^5 without computing.
The problem also mentions that 45^7 * 88^5 has 15 factors of 2. How is there 15 factors of 2??? I dont understand where 15 comes from.

How many do you get?

 

[JeffM]

You have placed this in advanced math so I presume you know about the laws of exponents and prime factorization.

[MATH]45^7 * 88^5 = (5 * 3^2)^7 * (2^3 * 11)^5 = 2^{15} * 3^{14} * 5^7 * 11^5.[/MATH]
Now what?

 

[kory]

Thank you for the help. I figured it out.

 

[lookagain]

I have to find the number of zeros in 45^7 * 88^5 without computing.

You meant to ask about how many trailing zeros it has or how many of
its rightmost digits are zeros without computing.