Question

What is the unit digit in $(7^{95}-3^{58})$?

• A. $0$
• B. $4$
• C. $6$
• D. $7$

Answer 1

Answer: (B)

$4$

Unit digit in $7^{95}=$Unit digit in $[{\left(7^4\right)}^{23}\times 7^3]$
=Unit digit in [Unit digit in ${\left(2401\right)}^{23}\times \left(343\right)$]
=Unit digit in $(1^{23}\times 343)$
=Unit digit in $343)$
$=3$
Unit digit in $3^{58}$= Unit digit in $[{\left(3^4\right)}^{14}\times 3^2]$
=Unit digit in [Unit digit in ${\left(81\right)}^{14}\times 3^2]$
=Unit digit in $[{\left(1\right)}^{14}\times 3^2]$
=Unit digit in $(1\times 9)$
=Unit digit in in $\left(9\right)$
$=9$
Unit digit in $(7^{95}-3^{58})$=$(7^{95}-3^{58})$$343-9)$=$(7^{95}-3^{58})$$\left(334\right)=4$
So, option B is the answer.