Question

Unit's digit in the number $(12357{)}^{655}$ is

• A. $1$
• B. $3$
• C. $7$
• D. $9$

Answer 1

Answer: (B)

$3$

The units digit of $(12357{)}^{655}$

The unit digit of 12357 which is 7 determines the value of the exponent $(12357{)}^{655}$

Therefore we have to find the unit digit of the exponent $7^{655}$ to find the unit digit of $(12357{)}^{655}$

We know, unit digit of $7^4=1$
Now, the units digit of $(12357{)}^{655}$

$=$ the unit digit of $7^{(4\times 163+3)}=7^{(4\times 163)}\times 7^3=1\times 3$
= $3$

Hence, option 'B' is correct.