Question

What number shall you get in the unit digit on solving the following problem:
\[ (6374)^{1793 \times (625)^{317} \times (341)^{491}} \]

• A. 0
• B. 1
• C. 2
• D. 3
• E. 4

Hint:

Shortcut: Any time an expression involves multiplying a term with a unit digit of 5 by any even number (like 2, 4, 6, 8), the resulting unit digit will always be 0.

Answer 1

The Correct Option is A

Step 1: Find the unit digit of each individual term.
For $(6374)^{1793}$, look at the last digit, 4. The cyclicity of 4 is 2 ($4^1=4$, $4^2=6$). Since the power 1793 is odd, the unit digit is $4$.
For $(625)^{317}$, look at the last digit, 5. The unit digit of 5 raised to any positive integer power is always $5$.
For $(341)^{491}$, look at the last digit, 1. The unit digit of 1 raised to any power is always $1$.

Step 2: Multiply the unit digits.
Product of unit digits = $4 \times 5 \times 1 = 20$.

Step 3: Determine final unit digit.
The last digit of the product 20 is $0$.