Question

(2^2)(3^3)(4^4)(5^5)(6^6)(7^7)(8^8)(9^9)(10^10)=?
?=

Answer 1

A large number. A more interesting question might be: without trying to calculate the number explicitly, how many zeros does it have at the end?

Answer 2

???

Answer 3

215779412229418562091680268288000000000000000

Answer 4

o0
0

Answer 5

I think i am mind struck

Answer 6

BTW, the answer to the question, how many zeros, as you see if 15.

But you can calculate it this way: how many zeros doest the integer p have at the end?

# of zeros
= # of factors of 10
= # of factors of 2 with matching # of factors of 5

In your number there are 5 factors of 5 from 5^5, and then another 10 factors of 5 from 10^10. Hence in total 15 factors of 5. there are certainly at least that many factors of 2, as they come from 2^2, 4^4, 6^6, 8^8 and 10^10.

Hence
15 = 10 + 5
= # of factors of 2 with matching # of factors of 5
= # of factors of 10
= # of zeros

Answer 7

THX, i learned alot!