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Student-Produced Response

If x is a positive integer, what is one possible value of the units digit of 1032x after it has been multiplied out?

Explanation:
For an integer, the units digit is the digit furthest to the right. It is sometimes referred to as the ones digit. For example, in a three-digit integer such as 125, the digit 5 is the units digit. In this problem, 1032x can be rewritten as (1032)x. The number 1032 has a units digit of 9. When a number with a units digit of 9 is raised to the x power, the resulting number will have a units digit of 1 (since 92 = 81) or a units digit of 9 (since 93 = 729). For all positive integer values of x, the units digit of 1032)x will be either 1 or 9.

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