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.

$13^1$ will give $3$ at the units place
$13^2$ will give $9$ at the units place, we get $9$ by taking the units digit of the result $3^2=9$
$13^3$ will give $7$ at the units place, we get $7$ by taking the units digit of the result $3^3=27$
$13^4$ gives $1$ at the units place, we get $1$ by taking the units digit of the result $3^4=81$
$17^2$ gives $9$ at the units place, we get $9$ by taking the units digit of the result $7^2=49$
$29^3$ gives $9$ at the units place, we get $9$ by taking the units digit of the result $9^3=729$
units digit of ($13^4$)($17^2$)($29^3$)=(units digit of $13^4$)(units digit of $17^2$)(units digit of $29^3$)
units digit of ($13^4$)($17^2$)($29^3$)=units digit of $(1)(9)(9)$
units digit of ($13^4$)($17^2$)($29^3$)=units digit of $81$
i.e. units digit of ($13^4$)($17^2$)($29^3$)=$1$
