5 to the power of 5 is divided by 5 to the power of 3
Answers
Step-by-step explanation:
There is a simple way to do this without having to compute 3^256. We do it through the singles digit of the number(Note that the units digit is the last digit in a number, representing the singlw number value of a digit. For example, 39908 has a units digit of 8 since 8 is a single value.) Here is how it goes.
3^1=3 so the last digit is 3
3^2=9 so the last digit is 9
3^3=27 so the last digit is 7
3^4=81 so the last digit is 1
3^5=243 so the last digit is 3
3^6=729 so the last digit is 9
3^7=2187 so the last digit is 7
3^8=6561 so the last digit is 1
And so on forever and ever with any base with a last digit of 3
As you increase the power of a number with a last digit of 3 by 1, this last digit pattern repeats. For the last number 3, this is 3,9,7,1 and so on where the units digit after increasing the power of 3 by 1 when the last digit is 1 makes the units digit go back to 3, just calculating this pattern for any number only requires the last digit anyways.
So we can make a sequence of this for units digit 3. (Yes, I am still explaining the problem above.)
For x being any either 0 or any positive integer:
4x+1 yields a units digit of 3
4x+2 yields a units digit of 9
4x+3 yields a units digit of 7
4x+4 yields a units digit of 1
The exponent of 3 is 256, which can be satisfied by 4x+4 for x being a positive integer. 4x+4=256 subtracting 4 from both sides gets 4x=252 which gets x=63. So we know that it is satisfied by the 4x+4 equation for a positive integer. Thus, the units digit is 1. Fun time! The units digits of all integer multiples of 5 are either 0 or 5. We could express assuming a units digit of 5 and get x remainder 6, but 5 can go into 6 without a negative so then we can assume a units digit of 0. We know that we would have to subtract 1 from 0 to get the units digit of 1 that we got from the sequence of units digits above. That means that the remainder is 1