Find the unit digit of (6374)^1793 × (625)^317 × (341)^491.

Given data

• We need only the unit digit of (6374)^1793 × (625)^317 × (341)^491.
• Assumption clarified: the notation (6374)1793 etc. denotes exponents, i.e., (6374)^1793, (625)^317, (341)^491.

Concept / Approach

• The unit digit of a power depends only on the unit digit of the base and the cycle of that unit digit.
• Unit digit cycles: 4 → (4, 6, 4, 6, …) period 2; 5 → always 5; 1 → always 1.

Step-by-step calculation

Units((6374)^1793) = Units(4^1793). Since 1793 is odd ⇒ units = 4.Units((625)^317) = 5 (any positive power of a number ending with 5 ends with 5).Units((341)^491) = 1 (any positive power of a number ending with 1 ends with 1).Product's unit digit = Units(4 × 5 × 1) = Units(20) = 0.

Verification

Because one factor contributes a terminal 5 and another contributes an even digit (4), the product ends with 0 regardless of other digits.

Common pitfalls

• Trying to compute large powers directly instead of using unit-digit cycles.
• Misreading the notation as multiplication rather than exponentiation.

Final Answer

0