Who is asking: Student
Level: Middle

Question:
If 57 is raised to the 28th power, what must be the units digit in the result?

If you raise 7 to the 500th power, what is the numeral that will appear in the units digit position?

Hi,

The first step is to experiment a little. Calculate 57² and 57³ = 57² 57 WITHOUT USING A CALCULATOR. Look at what you did. In calculating 57² you found 77=49 and that is all you needed to see that the units digit is 9. Now in calculating 57³ you found 79=63 and that is all you needed to see that the units digit of 57³ is 3. The point is that the digit 5 in 57 has no influence on the units digit of 57²⁸. To get the correct answer we could ask the seemingly simpler question, if 7 is raised to the 28th power, what must be the units digit in the result?

Now I suggest that you look at The units digit of 3 to the 58th power and The units digit of 2 to the power of 31921 to see how these problems are solved.

Cheers,
Penny

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