The last digit of the expression 3^101 X 7^202 is conclusively determined to be 7. This conclusion is reached by calculating the last digit using modular arithmetic, specifically through the application of mod 10. The calculations involve simplifying 3^101 and 7^202 using their respective cycles in mod 10, leading to the final result of 7.
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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?