If you raise 3 to the 324th power, what is the units digit of the result?

Question

can you please in explain in detail, how you got your answer

Answer 1

Look at the first few powers:

3^0 = 1
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
3^6 = 729
3^7 = 2187
3^8 = 6561

You'll see a pattern in the ones place (1, 3, 9, 7).

Divide the power by 4.

If the remainder is 0, there will be a 1 in the ones place.
If the remainder is 1, there will be a 3 in the ones place.
If the remainder is 2, there will be a 9 in the ones place.
If the remainder is 3, there will be a 7 in the ones place.

For example: 3^7
The power is 7.
7 ÷ 4 = 1 r 3     (r is notation for remainder)

Since the remainder is 3, there must be a 7 in the ones place.

3^7 = 2187 (as you can see, there is a 7 in the ones place)


324 ÷ 4 = 81 (no remainder), therefore there will be a 1 in the ones place.

Answer 2

3^0 = a million, 3^a million = 3, 3^2 = 9 , 3^3 = 27, 3^4 = eighty one, 3^5 = 243, 3^6 = ....9 ,3^7 = ...7 as you notice the final digits repeated are : a million , 3 , 9 , 7 so the digits are repeated interior the cycle of four. Now 324 is the 325th capacity simply by fact the 1st capacity is 0. in 325 this cycle of four is repeated eighty one cases leaving a million as a the rest. the final digit would be a million.