help! Options

[pAtRiCk_sTar]

aaacch i don't get this math problem, i'm really stupid. it's a junior high problem, so maybe someone could help?

Claire finished her assignment early, so her teacher suggested that she find the last digit of the product 3 x 3 to third power x 3 to fifth......x 3 to nineteenth. The entire product was too big for her calculator, but she still found the last digit. What is the last digit? Explain how she determined her answer

i know that if you add all the exponents, you'll get 3 to the 100th power, since
3+5+7+9+11+13+15+17+19=100 right (those are the exponent values...), so it'd be 3 to the 100th power. on my calc i got 5.153775207 to the 47th power.....what next?!?!!?

sorry if this is in the wrong board...i saw someone ask for math help awhile back, so i figured it'd be OK

[Spirited Away]

This page has something similar except with the number two instead. I'm reading it right now, but I think you'll find your answer there.

I can tell you now the it will end with one of these numbers: 1, 3, 9, 7...

3=3
3^2=9
3^3=27
3^4=81
3^5=243...
3^8=6561
3^12=531441

You'll notice that every 4th power give the same last digit. So powers of 4 8 12 16... should all have the same last digit. I think that I last digit should be 1 for the 100th power.

Okay, never mind.. I don't know how to do it.