What is the unit digit in the product of the following expression?
\(\left[(6374)^{1793} \times(625)^{317} \times(341)^{491}\right]\)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0
The unit digit of a product depends only on the unit digits of the numbers multiplied, so each power is reduced to its unit digit first.
\((6374)^{1793}\): powers of 4 end in 4 (odd power) or 6 (even power); 1793 is odd, so the unit digit is 4
\((625)^{317}\): every power of a number ending in 5 ends in 5
\((341)^{491}\): every power of a number ending in 1 ends in 1
Product of the unit digits: \(4\times5\times1=20\), so the unit digit is 0
Tip: A number ending in 5 multiplied by any even number always ends in 0, so once one factor ends in 5 and another is even, the answer is 0 without further work.