Question

What is the units digit of (13)^4(17)^2(29)^3 ?​

Answer 1

I think it is 7

Explanation:

Answer 2

Rewrite the product as

`13^4\cdot 17^2\cdot29^3 = (10+3)^4 (10+7)^2 (20+9)^3`

Powers of 10 and multiples of 10 don't contribute to the units digits, so we only need to consider the product

`3^4\cdot7^2\cdot9^3=81\cdot49\cdot729`

and we can treat this the same way:

`81\cdot49\cdot729=(80+1)(40+9)(720+9)`

Again, ignore the multiples of 10 to reduce this to the product 1*9*9 = 81, whose units digit is 1.