What is the units digit of $13^4\cdot17^2\cdot29^3$? 
What is the units digit of $13^4\cdot17^2\cdot29^3$?

I saw this on a GMAT practice test and was wondering how to approach it without using a calculator. Thanks.

If you compute modulo $10,$ then you'll get $$13^4 17^2 29^3 \equiv 3^4 7^2 (-1)^3\equiv -81\cdot49\equiv (-1)^2\equiv 1 (\mathrm{mod}~10).$$ Thus the last digit is $1.$
