Question

The last two digits of the number ${\left(23\right)}^{14}$ are

• A. $01$
• B. $03$
• C. $09$
• D. $17$

Answer 1

Answer: (C)

$(23{)}^{14}=(529{)}^7=(530-1{)}^7$
$={}^7{C}_0(530{)}^7-{}^7{C}_1(530{)}^6+\dots \dots .-{}^7{C}_5(530{)}^2+{}^7{C}_6(530)-1$
$=100K+7\times 530-1$
$=100K+3709$
$\Rightarrow$ last two digits are 09