What is the last digit of 2^2019 ?

This video shows a simple math skill to help you find the last digit of large exponents.
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[YeanYaneth-hleo]

I watch some vdo on my country that how to do but I don’t understand anything at all 😂 but when I saw ur vdo I feel better so thanks u sm ❤

[idkdikdidkd]

pleasure learning from Newton himself !

[devonspeaks]

All I can say is, "WOW!" Thank you so much. I just watched so many other videos and you explained it so well.

[AdminTubeZ]

Hi, can we use Euler's totient theorem to find the last 2 digits of 2^2019 and 2^2016?

[PumpkinHorn]

This makes more sense than what I put in my notes

[maricarsereno]

Thank God I found your video sir.🙂🥰. I find it hard to understand this lesson, not until I saw this.🙂

[navyaakkageorge]

That's a very beautiful explanation sir. Thanks a lot :)

[sackwqwokz]

Thank you for precise and concise explanation, sir. This video is very helpful.

[korboon]

Thank you so much without you I wouldn’t pass my exponent exam

[Nikioko]

The same as the last digit of 2¹⁹, 2¹⁵, 2¹¹, 2⁷ or 2³: 8

[kamehamehaaaaa]

Simple explaination to the point. Thanks

[PugboyMan]

This was very clear and helpful, you really deserves more subs :)

[Sacred_ray]

I watched the other videos of my country, but your video helped me a lot, thank you sir

[ultramegabarneyplayz]

WOW, I have searched so many youtube videos, and in this video I finally learned the steps you take to solve it. I thought this question was impossible before I watched this video. You are such a good math teacher!!!

[kayelabrador]

Sir, does units digit and last digit the same?

[holyshit]

2^2019 = 0 (mod 2)
2^2019 = 2^(4*504+3)(mod 5)

2^2019 = 0 (mod 2)
2^2019 = 3(mod 5)

We have system of congruences

x = 0 (mod 2)
x = 3(mod 5)

We can solve it with Chinese Remainder theorem
1 = 2*(3) + 5*(-1)
x = (2*(3)*3 + 5*(-1)*0)mod 10
x = 18 mod 10
x = 8 mod 10

[imawesome.]

what if we don't get a remainder? like for 9^2020
9^1 =9
9^2=81
9^3= 729
9^4= 6561

cycle= 9, 1, 9,

2020 divided by 4 = 505
but no what should i do?

btw your teaching is so fun!

edit: got it!!

[Problematica.]

Nice solution. Can you find the last three digits of the number of 19^97

[DEVILOP-fd]

Sir you helped me a lto today coz tommorow is my exam and i was bit confused with this topic you deserve it ❤️

[oliviagow-smith]

Thank you so much for this video! So helpful! I was wondering what I do if there's no remainder after dividing by the number of numbers in the sequence? Studying for my final! :)