Powerful Thinking 1

What pattern can you see in the last digits of the powers of 2?

What about the last digits of the powers of 3?

What patterns can you see in the last digits for the numbers in the picture?

Can you explain why all these numbers are multiples of 5?

What about the 99th powers 2^{99} + 3^{99}?

What can you find out about 1^{99} + 2^{99} + 3^{99} + 4^{99}?

What other patterns with powers can you find that have special properties?

Click here to download the POWERFUL THINKING 1 worksheet.

Click here for Notes for Teachers.

Also see Powerful Thinking 2, Powerful Thinking 3 and Powerful Thinking 4.

Click here for the poster.

These problems are adapted from the NRICH tasks Power Mad and Big Powers with permission of the University of Cambridge. All rights reserved.