Had to look up ‘Units digit’, have always called this the ‘ones digit’.
The first problem I usually encounter as a non-native english speaker is figuring out math terminologies. Like, what the hell is Units digit?
4^854 = 16^427 Since 6×6=36, any time you multipy two integers that end with digit 6, the product will also end with 6. Multiplying the product by a third integer ending with 6 must therfore also result in a new product ending with 6, etc. 4^854 = 16^427 is the product of 427 integers all ending with digit 6 and must therefore also end with digit six.
a simple trick: just multiply the base to the last digit. here, it would be 4*4 = 16. hence, 6 is in the unit's place. This helps because in Multiplication the last digit doesn't change. For example: 12 * 12 — 24 +120 — 144
Its clear that it is enough to check what happens mod 5, then: 4^854=(-1)^854=1 And the only possibility which is 1 mod 5 is 6.
I didn’t even know what a units digit was
If even power of 4 = unit digit 4 If odd power of 4 = unit digit 6
I swear I'm learning more in YouTube shorts than in school 💀
It's fun learning the terms in math in English. Your channel is great
I need reincarnation to learn math again
When life is less about solutions but more about patterns.
I can’t wait to use this in the real world!
Just divide the power with 4 .. remainder will be 2.. 4^2=16...unit digit =6 and if in any ques the remainder come 0 then unit digit will always be 1...
Brilliant! I never would have picked up on this pattern! Thank you!
854 can be written 4n+2 so 4 power 4n+2 that is 4 power 2 =16 unit digit is 6
When you start thinking of it as a logic puzzle instead of a math problem that is the secret to solving a lot of math problems.
I used to not like math at all. Now that I'm far beyond math in my studies, seeing these shorts every so often is actually very interesting!
Use the division rule of 4 to divide last 2 digits of the power i.e - 54÷4 = (4×13) + 2 »remainder in remaider table for base 4 the remainder colomn or the Square column has 6 . Hence 6 is answer!
There are patterns in the units digits of powers for several numbers. Here are some examples: 1. *Powers of 2:* - The units digit follows a cycle: 2, 4, 8, 6. 2. *Powers of 3:* - The units digit follows a cycle: 3, 9, 7, 1. 3. *Powers of 4:* - The units digit follows a cycle: 4, 6. 4. *Powers of 5:* - The units digit is always 5. 5. *Powers of 6:* - The units digit is always 6. 6. *Powers of 7:* - The units digit follows a cycle: 7, 9, 3, 1. 7. *Powers of 8:* - The units digit follows a cycle: 8, 4, 2, 6. 8. *Powers of 9:* - The units digit follows a cycle: 9, 1. 9. *Powers of 0 (except 0^0):* - The units digit is always 0. These patterns can be helpful when you need to quickly determine the units digit of a large power of a number.
@mecden1766