Find the last digit of 3^101 X 7^202

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The last digit of the expression 3^101 X 7^202 is determined to be 7. This conclusion is reached by calculating 147 mod 10 and using properties of modular arithmetic for powers of 3 and 7. Specifically, it involves finding the last digits of 3^4 and 7^4, which are then raised to the appropriate powers. The calculations confirm that the last digit remains consistent at 7. Therefore, the solution is correct.
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Homework Statement


find the last digit of 3^101 X 7^202

Homework Equations

The Attempt at a Solution


i have cal. that the last digit is 7 by...:
[147]mod10 X ([3^4]mod10)^25 X ([7^4]mod10)^25 = [7]mod10 X [1]mod10 = [7]mod10
so the last digit is 7

is it correct?
 
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cloveryeah said:

Homework Statement


find the last digit of 3^101 X 7^202

Homework Equations

The Attempt at a Solution


i have cal. that the last digit is 7 by...:
[147]mod10 X ([3^4]mod10)^25 X ([7^4]mod10)^25 = [7]mod10 X [1]mod10 = [7]mod10
so the last digit is 7

is it correct?

Yes.
 
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