What is the units digit of 6^15 - 7^4 - 9^3 ?

\(6^{15} - 7^4 - 9^3\)

\(= 6 - 1 - 9\)

\(= 6 - 10\)

\(= -4\)

Thus, Answer must be (C) 6

ScottTargetTestPrep
"Recall that we can add 10 (or multiples of 10) to a “negative” units digit to make it positive. Therefore, the actual units digit is -4 + 10 = 6"

Can you explain me this rule please?

hi guitarist Abhishek009 how is it possible that answer is 6 and not -4, can you pls explain the concept

thanks and have a great weekend

Just concentrating on the unit digits..
6-1-9
=6-(1+9)
=6-(0)
=6

Answer: C

I can help. So when we talk about numbers it is in the decimal system.
For e.g let us take the example of 20 - 11. So the unit place here would be 9. Or the unit place can be mathematically written as -1. But in the number form you won't write a negative integer.

Response:

Of course, a negative integer cannot be the units digit of any number; however, if a calculation involving units digit turns out to be a negative number, we can use the fact that adding 10 to any number does not change units digits to find an equivalent positive number.

Here’s an alternate explanation:

We found that the units digits of 6^15, 7^4 and 9^3 are 6, 1 and 9, respectively. To find the units digit of 6^15 - 7^4 - 9^3, rather than calculating 6 - 1 - 9, we can instead calculate 16 - 1 - 9 and find 6. Notice that we could also have taken 26 (or any number with a units digit of 6) instead of 16 and we would have found 26 - 1 - 9 = 16, which also has a units digit of 6.

Asked: What is the units digit of \(6^{15} - 7^4 - 9^3\)?

Unit digit of \(6^{15} = 6\)
Unit digit of \(7^4 = 1\)
Unit digit of \(9^3 = 9\)

Unit digit of \(6^{15} - 7^4 - 9^3 = 16 - 1 - 9 = 6\)

IMO C