## KrystaRenee What is the simplified form of the expression? k^16/k^8 1/k^8 k^24 k^8 k^128 one year ago one year ago

1. whpalmer4

$\frac{a^m}{a^n} = a^{m-n}$

2. jim_thompson5910

what whpalmer4 is saying is that you subtract the exponents

3. KrystaRenee

So the third option?

4. jim_thompson5910

you got it

5. jim_thompson5910

does that formula whpalmer4 wrote make sense and look familiar?

6. jim_thompson5910

I ask because I'm wondering if it's more helpful to write $\frac{a^m}{a^n} = a^{m-n}$ OR if it's just more helpful to write it out in english and say "subtract the exponents" or something like that

7. KrystaRenee

Honestly no.. And yeah, it is more helpful to write it out in English lol.

8. jim_thompson5910

that's good to know I guess all those letters and variables confuse and cloud things up a bit

9. KrystaRenee

Yes, they do.

10. jim_thompson5910

Even though the formulas are very confusing, it's helpful to know them because they say a lot without having to use any words and a lot of math books will use formulas instead of words

11. jim_thompson5910

so I recommend you practice more with reading formulas like $\frac{a^m}{a^n} = a^{m-n}$

12. KrystaRenee

Yeah, I know. I agree.

13. whpalmer4

Well, they make it quite clear that you can only do the subtraction if the base is the same. You cannot do the following: $\frac{3^3}{2^2} \ne 3^{3-2}$ and $\frac{3^3}{2^2} \ne 2^{3-2}$

14. jim_thompson5910

Alright, you probably already knew that before I even said anything, so that's great

15. whpalmer4

Whereas if you just remember "oh, yeah, subtract the exponents" you might well make that mistake.

16. jim_thompson5910

true, you make a good point there whpalmer4

17. jim_thompson5910

the bases have to be the same

18. ParthKohli

I do have problems memorizing formulas sometimes. But they are pretty helpful to memorize when you have to write your work down.

19. whpalmer4

And it makes sense if you look at it this way: $\frac{a^7}{a^4} = \frac{a*a*a*a*a*a*a}{a*a*a*a}$ Well, let's see, we count up the a's on the top, and we count up the a's on the bottom, and we cancel out the smaller quantity, and that leaves us with top-bottom a's, which of course is $a^{7-4}$

20. whpalmer4

But even if we agree that it is easiest to describe this one as "just subtract the exponents" you do have to get used to reading the formulas, because describing some of the other uses of exponents and especially logarithms isn't nearly so conducive to "plain English" descriptions!