College Mathematics

[tryingtesc]

I believe this is how it works. There's a rule involving multiplying exponents with the same base number, so:
8^(2x + y) is the same as
8^(2x) + 8^(y) which is the same as
8^x + 8^x + 8^y
= 15 + 15 + 25
= 55

If you would provide the correct answer, that would help with reverse engineering the rule/method, because I might be remembering the rule incorrectly.

You have the problem set up nicely, however, you should multiply in rows 2, 3, and 4 instead of add. You can "split" the exponent, but you then must multiply. For example: If you had x^2+3; that would equal (x^2)(x^3), the bases are the same and in multiplication you would simply add the exponents making it x^5.
You could not put them back together if you split them like this: x^2 + x^3. They would not be "like" terms, one is squared and the other cubed.

I hope this helps with your reverse engineering because I am not familiar with that method.

Best Regards,
Jason