what is the unit digit in (7^95 - 3^58) ?
powers of 7 end in 7,9,3,1,...
so, 7^95 = 7^92 * 7^3 -- it ends in 3
do a similar thing for powers of 3.
then do the subtraction.
To find the unit digit in (7^95 - 3^58), we need to calculate the value of 7^95 and 3^58 first.
To calculate the unit digit of powers of a number, we only need to consider the unit digit of the base number, and the pattern it follows. Let's start with 7^95:
The unit digit of powers of 7 repeats in a pattern: 7, 9, 3, 1. So we can divide 95 by 4 (the length of the pattern) to find the position of the unit digit in the pattern.
95 ÷ 4 = 23 remainder 3
This means that the unit digit of 7^95 is the same as the third position in the pattern, which is 3.
Now let's calculate 3^58:
The unit digit of powers of 3 also repeats in a pattern: 3, 9, 7, 1. Again, we divide 58 by 4 (the length of the pattern):
58 ÷ 4 = 14 remainder 2
This means that the unit digit of 3^58 is the same as the second position in the pattern, which is 9.
Finally, we subtract 3^58 from 7^95: 3 - 9 = -6.
However, we are only interested in the unit digit. So we can convert -6 to its equivalent positive unit digit, which is 4.
Therefore, the unit digit in (7^95 - 3^58) is 4.