Can you SOLVE?

Added: 2026-05-28

[00:00:00]I'm ready.

[00:00:01]Today's problem is to find the unit digit of 4 to the power 29 to the power 30 minus 4 to the power 30 to the power 29. So, what we will do is first we'll find what are the unit digits when we raise 4 to any number. So, let us see the the power of 4 and the number that you get and the unit digit.

[00:00:35]So, 4 to the power 1 the number is 4 and the unit digit is 4.

[00:00:40]4 to the power 2 the number you get is 16 the unit digit is 6.

[00:00:47]4 cubed the unit digit we'll find out 4 cubed is 64. So, the unit digit is again 4. 4 to the power 4 the number is 256 and the unit digit is 4. So, you can see here that whenever we raise 4 to a odd power you get the unit digit as 4 and when you raise 4 to a even power we get the unit digit as 6. So, what we have is 4 to the odd power the unit digit is nothing but 4 and 4 to the even power the unit digit is 6. This is what we have to make a note of. Now, when we are Let us see now here what are the powers.

[00:01:43]When we take 29 to the power 30 we are taking 29 to the power 30 is it odd or even?

[00:01:58]Odd number multiplied by another odd number is always going to give you a odd number. So, this is odd.

[00:02:07]So, 4 to the power 29 to the power 30, unit digit is 4 to the odd power, and for odd power, the unit digit is 4.

[00:02:24]Now, let us see 30 to the power 29.

[00:02:31]30 to the power 29, what type of a number is it?

[00:02:35]30 is a even number, and you multiply even number by another even number, you will always get a even number. So, 30 to the power 29 is a even number. So, 4 to the power 29 to the power 30, unit digit is nothing but 4 to a even power, so it is going to be 6.

[00:03:05]Now, when we find out what is the unit digit of unit digit of 4 to the power 29 to the power 30 minus 4 to the power 30, you can see first we have to take 29 to the power 30, and here in both the cases, here this I have written incorrectly. This is going to be nothing but 4 to the 30 to the power 29.

[00:03:50]And this is 4 to the 29 to the power 30 minus 4 to the 30 to the power 29. And this is unit digit of What will we do? We will subtract the two unit digits.

[00:04:08]So, it is 4 to the power 29 to the power 30 minus unit digit of 4 to the power 30 to the power 29. And this turns out to be 4 minus 6. So, you are subtracting a bigger number from a smaller number. You cannot do that, so you will borrow 10 from the tens place. So, it will be nothing but 10 plus and 4 minus 6 is nothing but 2, so it is 10 minus 2, which is nothing but 8. So, we get that the unit digit of this number is nothing but 8. The question it looked very difficult that perhaps we have to find the value of the numbers and then subtract them, but it is not like that. You can just find the unit digits and subtract them, and this is what we did did. And in the case of 4, it is very simple. The unit digits are oscillating between 4 and 6, and we get this simple result that 4 raised to any odd power is 4 and 4 raised to any even power, the unit digit is 6.