## randomecorner one year ago what value of p solves the eqatian? p^-5=1/243

1. randomecorner

i need help big time

2. Nnesha

this is like 5th time ii'm looking at this (exact same ) question

3. Nnesha

familiar with the exponent rule ? $\huge\rm x^{-m} =\frac{ 1 }{ x^m}$

4. randomecorner

nope

5. randomecorner

its 3 right?

6. Nnesha

x^{-m} is same as $\huge\rm \frac{ x^{-m} }{ 1 }= \frac{ 1 }{ x^m }$ flip the fraction to convert negative to positive exponent

7. randomecorner

so it is 3

8. Nnesha

how did you get that ? plz explain

9. randomecorner

3*3*3*3*3=243

10. Nnesha

alright nice what about $\huge\rm p^{-5}$how would you get rid of the negative exponent ?

11. randomecorner

1/3

12. Nnesha

no just p^{-5}

13. Nnesha

remember flip the fraction and change the sign of exponent ?

14. randomecorner

wow thx

15. randomecorner

i feel dumb lol

16. Nnesha

well you're not

17. randomecorner

some of these math problems get fustrating

18. randomecorner

so the answer is 3 or 1/3?

19. Nnesha

well need to pay attention i'll give u an example $\huge\rm a^{-2} = \frac{ 1 }{a^2 }$

20. Nnesha

so $\rm p^{-5}= ?$

21. randomecorner

i was making sure because on the thing its a box to type the answer in

22. randomecorner

p^-5=3

23. Nnesha

or you can substitute p for 1/3 and then for 3 to check ur answer you should get equal sides at the end

24. Nnesha

how would you convert p^{-5} to positive exponent ?

25. randomecorner

flip the eqation

26. Nnesha

yes right how would you do that p^{-5}/1 = ?

27. randomecorner

-5\p=1\3

28. randomecorner

//

29. randomecorner

s in the box it is 1/3? or 3 k12 is usally not settled about that

30. Nnesha

how did you get 1/3

31. Nnesha

3* 3*3*3*3 = 243 right agree ?

32. randomecorner

imso confussed again sorry

33. randomecorner

and also 1/3 goes into 1/243 5 times

34. Nnesha

when you multiply same bases we should add their exponents so $\huge\rm 3^1 \times 3^1 \times 3^1 \times 3^1 \times 3^1 =3^{1+1+1+1+1}$

35. randomecorner

yes

36. Nnesha

so $\huge\rm p^{-5} = \frac{ 1 }{ 3^5 }$ now move 3^5 at the numerator flip the fraction when you do that sign of the exponent would change

37. Nnesha

or in other words what is the reciprocal of 1/3^5 ??

38. randomecorner

1/15?

39. Nnesha

it's $\huge\rm \frac{ 1 }{ 3^5 }$ 3 to the 5th power not 3 times 5

40. randomecorner

sorry that's what i should of wrote insted

41. Nnesha

okay so when you flip 1/3^5 what would you get ?

42. randomecorner

1/243

43. randomecorner

44. Nnesha

well we changed 243 to 3^5 you should remember these exponents rule $\huge\rm x^{-m} =\frac{ 1 }{ x^m } ~~and~~ \frac{ 1}{ 2^{-m} }= 2^m$ you have to flip the fraction to change negative to postiive exponent

45. Nnesha

i've few mints have to go

46. Nnesha

well yes $3^{-5} = \frac{ 1 }{ 3^5 }$

47. Nnesha

which is equal to right side