Here,

First we need to know the power of 3

\(3^1 = 3\) --------------unit digit = 3

\(3^2 = 9 \)--------------unit digit = 9

\(3^3 = 27\) --------------unit digit = 7

\(3^4 = 81\) --------------unit digit = 1

\(3^5 = 243\) --------------unit digit = 3

We can see in the power of 3, unit digit repeats after 3, 9, 7, 1. we have 4 terms

As per ques, it is given \(23^{25}\)

just concentrate with the unit digit 23 i.e 3.

since, after every 4th term in the power of 3, repeats itself i.e 3,9,7,1,3

so, divide \(\frac{25}{4} \) and the reminder is 1, ( 25 is the power of 23, given in the ques. If the power is 36 then we divide 36 by 4)

that means we need the 5th term


the 5 term from the 3,9,7,1,3 will be 3 (unit digit),

similarly, 6th term will be 9,

7th term will be 7

8th term will be 1 and so on...........

so, the unit digit for \(23^{25}\) = 3

and we know 3 -3 = 0 , so the unit digit for \(P=23^{25}-23 = 0 \)