I am currently in the process of taking the GMAT to apply to grad school. I am about to take it for the third time and have a question, one that I have seen on the test every time, that I have never been able to answer. How can one determine the last digit of a large exponent by hand. I have seen several examples of how to do this by breaking it up into smaller exponents, but is there a formula or some common things to look for? Thanks for any help.
I am guessing this is a level 10 -12 question.
Landon
Hi Landon,
There is no formula but there is a pattern that will show you how to find the last digit. For example "What is the last digit of 7358?"
Suppose that you are going to construct a table with 358 rows and record last digit of the the 358 powers of 7. Start the table, either using either your calculator or doing the arithmetic by hand.
| Power of 7 | Last digit |
|---|---|
| 71 | 7 |
| 72 | 9 |
| 73 | 3 |
| 74 | 1 |
| 75 | 7 |
| 76 | 9 |
| 77 | 3 |
| 78 | 1 |
| 79 | 7 |
Notice the pattern of the last digits. They are 7,9,3,1,7,9,3,1,7,9,... The last digit repeats in a pattern that is 4 digits long, 7,9,3,1.
If you complete the table for 358 rows how many times will this pattern repeat? 358 divided by 4 is 89 with a remainder of 2 so the pattern will repeat 89 times and then there are two more rows. These rows then have 7 and 9 in the second column so the last digit of 7358 is 9.
Penny