Find the unit digit of (474)^153?

Question

Answer

Unit Digit of (474)^153

When finding the unit digit of a number raised to a large power, we only need to consider the unit digit of the base number.

Step 1: Find the pattern of unit digits

For 474, the pattern of unit digits when raised to powers is: 4, 4, 4, 4, ...
Since the pattern repeats every 1 power, we can simplify the problem by finding the unit digit of 474^1.

Step 2: Find the unit digit of 474^1

Step 3: Determine the unit digit of the given power

153 divided by 1 leaves a remainder of 0.
Since the pattern repeats every 1 power, the unit digit of (474)^153 is the same as the unit digit of (474)^1, which is 4.

Conclusion