(192^3)(5^19)

Question

(192^3)(5^19)

anonymous · Answer

What is the sum of the digiits of the number (192^3)(5^19) when the number is written in standard form (that is, when everything is multiplied out)?

turingtest · Answer

@FoolForMath seems like your type of Q here

anonymous · Answer

Problem source?

anonymous · Answer

pardon?

anonymous · Answer

From where does this problem originated?

anonymous · Answer

it was a problem on a test

anonymous · Answer

Yes, which test?

anonymous · Answer

lol...it's a problem solving course

anonymous · Answer

Olympiad?

anonymous · Answer

huh?

anonymous · Answer

The answer is 9. 

Hint: There are many zeros. Can you find how many?

turingtest · Answer

IMO problem?
apparently not...
lol I wanna take a "problem solving" course too if it will teach me how to do this kind of thing

anonymous · Answer

Extra hint for my dear Turing: 

Break each term into primes and then ;)

turingtest · Answer

ah$$3^3\cdot2^{18}\cdot5^{19}=5\cdot 3^3\cdot10^{18}$$

turingtest · Answer

FFM makes it look so easy
thanks!

anonymous · Answer

That's right Turing!

$$ 192^3\times 5^{19}=2^{18} \times 3^3 \times 5^{19} = 27\times 5 \times 10^{18} = 135 
\times  10^{18} $$

turingtest · Answer

I need to learn how to approach these kinds of things; I always feel like I don't know what approach to take and a get paralyzed.

with people like you around @FoolForMath I think I'm getting a little more comfortable with these, so thanks again =)

anonymous · Answer

Turing is too kind and modest, I am just another ordinary Fool.