This math skill teaches how to determine the ones digit of an expression involving exponentiation by identifying and using patterns in the digits. For any base ending in 5, the ones digit of its powers remains 5. For bases ending in other digits like 7, the ones digit follows a repeating pattern that can be utilized to find the ones digit of higher powers.
Toggle Auto Play (On)
Audio Voice (Mobius Voice)
Toggle Teaching (Video)
Ones digit of an exponent multiplication, through following a pattern
Test your understanding of ones digit of an exponent multiplication by practicing it! Work through the below exercises to use it in practice.
🎙️
What will the ones digit of this expression be?
🎙️
First let's look at the 5s, every time a number with a ones digit of 5 is multiplied by 5, the product also has a ones digit of 5. So 5 to the power of 11 will have a ones digit of 5.
🎙️
For the 7s, it's a bit different. 7 to the power of 1 is just 7, 7 to the power of 2 is 49, so a ones digit of 9. 7 to the power of 3 would have a ones digit that is determined by 9 times 7, so that would be 3, and 7 to the power of 4 would be determined by 3 times 7, which would have a ones digit of 1. After that, 1 times 7 is back to 7 again.
🎙️
So we have a 4 item repeating pattern. 7 to the power of 8 is the eighth value in this pattern, which is 1.
🎙️
For our original question, we now know that it's a ones digit of 5 multiplied by a ones digit of 1, for a final ones digit of 5.