How many zeros are at the end of457 · 885?Explain how you can answer this question without actually computing the number. (Hint:10 = 2 · 5.)When this number is written in ordinary decimal form, each 0 at its end comes from a factor of , or one factor of 2 and one factor of .Since there are factors of 2 and factors of 5, there are exactly factors of 10 in the number. This implies that the number ends with zeroes.

The right format of the number is (45^8)(88^5).

There are 8 zeros

Step-by-step explanation:

Using the unique factorization of integers theorem, we can break any integer down into the product of prime integers.

So breaking it down we have;

(45^8) = (3 x 3 x 5)^(8)

(88^5) = (2 x 2 x 2 x 11)^(5)

Now, if we put it back together as separate factors, we'll get;

(3^(16)) x (5^(8) ) x (2^(15)) x (11^(5))

Now let's find the number of zeroes by figuring out how many factors of 10 (which equals 2 x 5) we can make. Thus, we can make 8 factors of 10 so it looks like;

(3^(16)) x (2^(7)) x (11^(5)) x (10^(8))

Thus, we can see that there will be 8 zeros as the end is (10^(8))

df =

both have same length