wchin24 wrote:

Firstly, thanks for having these questions - they are a great help!

Wanted to ask, though, about the question below:

7)What is the units digit of 23^99∗14^352+9002^1003∗918^437986

I keep getting 7 * 1 + 8 * 4 = 9. I'm using cyclicity here. Thanks in advanced.

Hey

wchin24 ,

The mistake you did is highlighted above.

14^352

The pattern of 4 is 4,6

This means cyclicity is 2.

When you divide the power with 2, you will get 0 remainder. That means last digit is last place of the pattern, which is 6 here.

Hence, the last digit of 14^352 is 6.

Does that make sense?

OMG YES! Thank you! I was tripping up since I was seeing it as 4^0, but in reality this just means that it'll end up at the last place of the pattern here.