powerful-thinking2Investigate the last digits of the numbers in the picture when n = 1, 2, 3 , 4 and 5. What do you notice? Does this pattern continue? Why?

Will the first number \(2^n + 3^n\) be a power of 10 for any value of n?

What can you say about the values of n that make the second number \(3^n + 7^n\) a power of 10?

Are there any other pairs of integers between 1 and 10 which have similar properties?

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