Question
Question: The last two digits of the number (23)<sup>14</sup> are...
The last two digits of the number (23)14 are
A
01
B
03
C
09
D
None of these
Answer
09
Explanation
Solution
(23)14 = (529)7 = (530 – 1)7
= 7C0 (530)7 – 7C1(530)6 + ……– 7C5(530)2 + 7C5 (530) – 1
= 7C0(530)7 – 7C1(530)6 +……+ 3710 – 1
= 100m + 3709
\ last two digits are 09