The digit in unit’s place of the product (2153)^167 is:radio_button_unchecked1radio_button_unchecked3radio_button_unchecked7radio_button_unchecked9
Question
The digit in unit’s place of the product (2153)^167 is:
- radio_button_unchecked 1
- radio_button_unchecked 3
- radio_button_unchecked 7
- radio_button_unchecked 9
Solution
To find the digit in the unit's place of the product (2153)^167, we only need to consider the last digit of the base number, which is 3 in this case.
The pattern of the last digit of the powers of 3 is as follows:
3^1 = 3 3^2 = 9 3^3 = 7 3^4 = 1 3^5 = 3 3^6 = 9 3^7 = 7 3^8 = 1 ...
As you can see, the pattern repeats every 4 powers.
So, to find the last digit of (2153)^167, we need to find the remainder when 167 is divided by 4.
167 divided by 4 gives a quotient of 41 and a remainder of 3.
Therefore, the last digit of (2153)^167 is the same as the last digit of 3^3, which is 7.
So, the digit in the unit's place of the product (2153)^167 is 7.
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