Question

Find the unit digit of $(7^{95}-3^{58})$.

• A. $6$
• B. $4$
• C. $3$
• D. None of these

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 $\left(343\right)$

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 $\left(9\right)$
$=9$

Unit digit in $(7^{95}-3^{58})=$ Unit digit in $(343-9)=$ Unit digit in $\left(334\right)=4$