## anonymous one year ago Simplify 11 to the negative 4th power over 11 to the 8th power. 1 over 11 to the 12th power 1 over 11 to the 4th power 114 1112

1. anonymous

@phi

2. phi

$\frac{11^{-4} }{11^8}$

3. anonymous

yup

4. phi

can you rewrite the 11^-4 so we get a +4 ? (remember how to do that ?)

5. anonymous

yes we flip

6. anonymous

i think it would be 1/11^4

7. phi

yes. so we now have $\frac{1}{11^4} \cdot \frac{1}{11^8} = \frac{1}{11^4\cdot 11^8}$

8. anonymous

yup

9. phi

11^4 means 11* 11*11*11 11^8 means 11*11*11*11* 11*11*11*11 what do we get when we multiply that all together?

10. anonymous

121

11. phi

?

12. anonymous

you said when we multiply it together?

13. phi

I don't mean multiply it out and get a number. just show them being multiplied like this 11* 11*11*11 * 11* 11*11*11* 11* 11*11*11

14. anonymous

oh woops lol sorry

15. phi

people use exponents to write that in short-hand. can you ?

16. anonymous

umm idk what short hand is

17. phi

we have 11 times itself how many times ? 11* 11*11*11 * 11* 11*11*11* 11* 11*11*11

18. anonymous

12 times

19. phi

and how do we show that using exponents?

20. anonymous

11^12?

21. phi

yes. notice that is easier to type than 11* 11*11*11 * 11* 11*11*11* 11* 11*11*11

22. anonymous

way easier

23. anonymous

24. phi

so here is what you have $\frac{11^{-4} }{11^8}= \frac{ 1}{11^{4}\cdot 11^8}= \frac{1}{11^{12}}$

25. anonymous

yup

26. phi

you should notice that 11^4 * 11^8 means 11* 11*11*11 * 11* 11*11*11* 11* 11*11*11 but it is faster to say: 4 11's and 8 11's is 12 11's in other words, notice the short cut: 4+8 =12 11^4 * 11^8 = 11^12

27. anonymous

mmmhhh

28. anonymous

it takes up space ifyou write it out also

29. phi

the thing you should try to remember is when multiplying, you can add the exponents. that is the short cut they want you to learn.

30. anonymous

oh

31. anonymous

ok

32. anonymous

33. phi

yes and if they were being trick the answer could also be 11^(-12)

34. anonymous

yuppp

35. anonymous

thanks again and i have like 2 or 3 more if you can still help it would be great

36. phi

new post

37. anonymous

ok