## anonymous one year ago What is the value of the expression? 5^-6*5^2 ---------- 5^-8 A. 5^−20 B. 5^−12 C. 5^4 D. 5^-4

1. Nnesha

exponent rule $\huge\rm \frac{ x^m }{ x^n }=x^{m-n}$ there is negative exponent in the denominator so move that to the top

2. anonymous

....

3. Nnesha

sorry i don't understand dot language.

4. anonymous

lol sorry It's just I don't get it :'(

5. Nnesha

basses are same so just transfer -8 to the top here is an example $\large\rm \frac{ 2^3 }{ 2^{-5} } = x^{2\color{red}{+}5}$

6. anonymous

ok

7. Nnesha

and then apply exponent rule $\huge\rm x^m \times x^n = x^{m+n}$when you multiply same bases you should add their exponents

8. anonymous

ok

9. Nnesha

so what did you get ?

10. anonymous

7?

11. Nnesha

how did you get that ?

12. anonymous

2+5

13. anonymous

im so wrong! I'm sorry i'm being stupid

14. Nnesha

i know ... reread what i said above then try to solve

15. anonymous

ill just put d bye

16. Nnesha

you should familiar with the exponent rules you can't have the negative exponent there $\huge\rm x^{-m}=\frac{ 1 }{ x^m }$

17. anonymous

???

18. Nnesha

$\huge\rm \frac{ \color{Red}{5^{-6} \times 5^{2} }}{ 5^{-8}}=$ first look at the numerator when you multiply same bases you should ADD their exponents $\large\rm x^m \times x^n = x^{m+n}$

19. anonymous

8?

20. Nnesha

-6+(2) = 8 ?

21. anonymous

-4

22. Nnesha

yes right $\huge\rm \frac{ 5^{-4} }{ 5^{-8}}$ now move the -8 exponent to the top here is an example $\huge\rm \frac{ x^m }{ x^{n} } = x^{m+(-n)}$

23. anonymous

i divide now?

24. Nnesha

now you don't divide bases are the same right 5 is base and there is negative -8 exponent in the denominator move that to top of the fraction

25. anonymous

huh

26. Nnesha

here is an example $\huge\rm \frac{ 2^{-3} }{ 2^{-9} } = 2^{-3+(-9)}$

27. anonymous

28. Nnesha

that's an example and there is typo wait a sec

29. anonymous

oh

30. Nnesha

here is an example $\huge\rm \frac{ 2^{-3} }{ 2^{-9} } = 2^{-3-(-9)}$

31. anonymous

oh subtract?

32. anonymous

its 6

33. Nnesha

yes right - times -9 is = positive 9 so -3 +9 now look at ur question $\huge\rm \frac{ 5^{-4} }{ 5^{-8} }= 5^{???}$

34. anonymous

-12

35. Nnesha

no remember sign would change

36. Nnesha

$\huge\rm \frac{ 5^{-4} }{ 5^{-8} }= 5^{-4-(-8)}$

37. anonymous

6?

38. Nnesha

how did you get 6 ?? :O

39. anonymous

IDK

40. Nnesha

so why did you say 6 ?? just add the exponent that's it

41. anonymous

4

42. Nnesha

$\huge\rm \frac{ 5^{-4} }{ 5^{-8} }= 5^{\color{Red}{-4-(-8)}}$ know how do solve red part(exponents ?

43. Nnesha

yes right!!

44. anonymous

so its c

45. anonymous

???

46. Nnesha

ye...

47. anonymous

tysm!!!

48. Nnesha

YW