Question

If $n={\left(33\right)}^{43}+{\left(43\right)}^{33}$, what is the units digit of $n$?

• A. $0$
• B. $2$
• C. $4$
• D. $6$
• E. $8$

Answer 1

Answer: (A)

$0$

Lets, first find the cyclicity of unit digit of 3. which is (3,9,7,1)

Now convert exponent value in to multiple of 4.

here $43=4\left(10\right)+3$ so take $3^3$ as unit value of first term which is 27 ===> unit digit is $7$

Now $33=4\left(8\right)+1$,so take $3^1$ as unit value of second term which is 3 ====> unit digit is $3$

Now unit digit of n = unit digit of first term + unit digit of 2nd term = $7+3=10$ = unit digit is $0$