Question

Q.No : 23. Find the unit digit [162^162x197^160]+[543^540+698^638]

Answer 1

Solution:

We have to find the unit digit of

$[162^{162}\times 197^{160}]+[543^{540}+698^{638}]$

As the unit digit of , $162^{162}$ = 4 , ∵ unit digit of $2^5 is 2 .$

→162 = 32 × 5 + 2

$162^{162}$= $162^{32\times 5 +2}= 2^2=4$→Unit Digit

Now, $197^{160}= 197^{40\times 4}= 7^{4}=1$→ Unit Digit

→${543}^{540}={543}^{4 \times 135}$ ⇒As unit digit of 3^4 is 1.So unit digit of {543}^{540} will be 1.

$698^{638}= {698}^{5 \times 127 + 3}$ : As 8³ have unit digit 2, so

$698^{638}$ will have unit digit 2.

→ 4 × 1 + (1 +2)

= 4 + 3

= 7

→So, 7 is the unit Digit of $[162^{162}\times 197^{160}]+[543^{540}+698^{638}]$