## anonymous one year ago What is the missing exponent?

1. anonymous

2. anonymous

Ok, we still work in the correct order of operations. In other words, let's work with the denominator first.$\left(8^{-7}\right)^2 = 8^{-7}\times8^{-7}$Here, you are multiplying, so what should that simplify to? (aka $$8^{??}$$)

3. anonymous

8^0???

4. anonymous

When you multiply, you add the exponents. You would get $$8^0$$ if you subtracted them.

5. anonymous

oh ok so its 8^-14

6. anonymous

Yes. So, plugging that in again, $\frac{8^{-5}}{8^{-14}} = 8^{?}$ We are dividing here.

7. anonymous

dividing which ones

8. anonymous

(im putting my baby bro. to sleep right now so i might type slow i only have 1 hand)

9. anonymous

1 hand free*

10. anonymous

(That's fine.) You're dividing in general, so you're going to have to either add or subtract the exponents. When you multiply, you added, so when you divide, you...?

11. anonymous

subtract

12. anonymous

so 8^9

13. anonymous

14. anonymous

Yes! Also, just in general, the only time you will multiply exponents (with the same bases, like here where you had 8 on the bottom) is when you have something like $$\left(8^3\right)^2$$. This would simplify to $$8^6$$ because what you're doing is $$8^3 \times8^3$$.

15. anonymous

ok tysm! You're so smart :D

16. anonymous

So, for you to write down, you can say $$\left(a^b\right)^c = a^{bc}$$

17. anonymous

i did

18. anonymous

I GOT A 100!!!!!!!!!!

19. anonymous

Good job!! :)

20. anonymous

tysm!!! i gtg bye

21. anonymous

np