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

[whomps]

I think the last digit is going to be 1.

Because uh.. for every even number exponent, the last digit changed from 1 to 9.

3^2 = 9
3^4 = 81
3^6 = 729
3^8 = 651
3^10 = 59049
3^12 = 531441

So I wrote all the even numbers up to 100 and basically patterned it out. Haha.

BUT all the exponents divisible by 4 have a last digit of 1. And 100 is divisible by 4 so the last digit should be 1.