A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Which expression is equivalent to (7^3)−2? 1 over 7 times 7 times 7 times 7 times 7 times 7 7 1 over 7 negative 1 over 7 times 7 times 7 times 7 times 7 times 7

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @phi

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @IrishBoy123 @imqwerty

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I need help with some exponent questions if you can help that'd be awesome

  4. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    what does a negative exponent mean ? any idea ?

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Just like a regular exponent just negative?

  6. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    there is a long explanation of why it is so, but cutting to the chase \[ a^{-b}= \frac{1}{a^b} \] and \[ a^{b}= \frac{1}{a^{-b}} \]

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm i get confused with fractions and exponents so I really dont know

  8. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    that "rule" says: flip the fraction *and* negate the exponent.

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    This is a combo of both lol

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm

  11. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    you can learn it if you have time try guessing what \( 2^{-1} \) is. (flip it and negative the exponent)

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its a negative exponent?

  13. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \( 2^{-1} \) has an exponent of -1 you can "rewrite it" by 1) flipping it 2) make the exponent -(-1) = +1

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ..

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the 1 is the exponent?

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    right

  17. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    can you rewrite \( 2^{-1} \) ?

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    umm

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    maybe

  20. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    flip (invert) means if you have a, write 1/a if you have 1/a write a if you have (stuff) write 1/(stuff)

  21. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so like 1-2?

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    like the - sign is negative?

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i do not get it D:

  24. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    2^(-1) first step: FLIP 1/2^(-1)) second step: change the exponent -1 to -(-1) (which simplifies to 1) we get 1/2^1 or just 1/2

  25. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[ 2^{-1} = \frac{1}{2^1} = \frac{1}{2} \]

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so the 2^-1 would be 1^-2?

  27. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or the 1/2

  28. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok i think i got that

  29. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    if you just had 3 \[ 3 \text{ flipped is } \frac{1}{3} \]

  30. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so instead of 1^-3 itd be 1/3??

  31. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    ok, one more \[ 3^{-2} \] can you flip and negate the exponent?

  32. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lets see

  33. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2/3?

  34. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or 2^-3?

  35. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ya 2/3 that would be correct i believe

  36. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    none of those. you don't change 3^-2 when you flip it rather, we think of it as \[ \frac{3^{-2}}{1} \] and swap top and bottom to flip it. then change the -2 to +2

  37. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    mm

  38. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its still really confusing

  39. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    let's try this flip 1/2

  40. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1^2?

  41. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1^-2

  42. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im sorry D:

  43. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    in \( \frac{1}{2} \) what is the top number ?

  44. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the 1

  45. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    and 2 is the bottom number. what do you get if you swap those ?

  46. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2/1

  47. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    and what do you get if you flip 2/1 ?

  48. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1/2?

  49. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yes can you flip 1/3 ?

  50. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohhhh ok 31

  51. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3/1*

  52. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yes

  53. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ahhhhh ok

  54. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    normally when we flip a number, say 2 to 1/2 we get different numbers. (2 is not 1/2) but if we *also* change its exponent, we get the same number

  55. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    mm

  56. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    in other words \[ 2^{-1}\] if we flip it , to get \( \frac{1}{2^{-1}} \) and then change the -1 to +1, \[ 2^{-1}=\frac{1}{2} \]

  57. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so we pretty much eliminate the -1? if we do +1?

  58. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    another example \[ 2^{-5} = \frac{1}{2^5} \]

  59. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  60. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then if we changed the exponent to +5 it'd go as 1/2?

  61. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    I don't understand the question. can you ask in a different way?

  62. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm so the 1/2-5

  63. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if we changed the -5 to +5 then instead of 1/2-5 it would be 1/2?

  64. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[ \frac{1}{2^{-5}} \] 1) flip it and 2) change the sign on the 5 we get \[ \frac{1}{2^{-5}} =2^5\]

  65. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  66. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    still really weird to me

  67. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    it all makes sense (once you learn what is going on) but for the moment, just learn the rules 2^5 can be written as 1/2^-5 2^-5 can be written as 1/2^5

  68. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  69. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[ (7^3)^{−2}\] can you rewrite this? (tread the (7^3) as one thing)

  70. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    *treat

  71. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok umm 3/7

  72. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    leave (7^3) alone. it is one thing. keep it one thing. but if we do (7^3)^ -2 what can we do to make the -2 positive ?

  73. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok lets see

  74. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i believe flip the numbers around? I really dont know DD:

  75. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yes flip. think of (7^3) as one "number"

  76. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  77. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so 3/7^-2?

  78. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or 3^7-2

  79. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    you changed (7^3) . don't change it.

  80. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohhh

  81. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    7^3 stays the same

  82. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if we made it different it would be 7/3^2?

  83. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yes, what changes is we write 1/(7^3)^2

  84. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohhhh

  85. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so the 7 stays with the 3

  86. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok ok

  87. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    we now have \[ \frac{1}{(7^3)^2}\]

  88. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ya

  89. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    do you know that x^2 means x*x ?

  90. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no i didnt

  91. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    do you know that 3^2 means 3*3 ?

  92. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  93. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    and 5^2 means 5*5

  94. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  95. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    what about (7^3)^2 any idea ?

  96. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm

  97. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I was think 7x3x2 but that wouldnt be correct right

  98. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    use the same pattern as 2^2 = 2*2 3^2 = 3*3 4^2 = 4*4 x^2 = x*x y^2 = y*y do you see how to do (7^3)^2 ?

  99. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    7x3 and 3x2?

  100. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    would you believe (7^3)*(7^3) ?

  101. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thats how it is??

  102. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    there is only 1 7^3

  103. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    if you have something and want to say: multiply by itself 2 times, you write (something)^2 and that is short for something * something

  104. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmmm ok

  105. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    so you want to show (xyz) times itself 3 times you would write (xyz)^3

  106. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  107. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so it would be 7x7x7?

  108. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if I understand correctly or 7x3?

  109. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    7^3 means 7*7*7

  110. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok i got that

  111. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    so (7^3)^2 means (7^3)*(7^3) and 7^3 means 7*7*7 so we can say (7*7*7)*(7*7*7) or just 7*7*7*7*7*7 so \[ \left(7^3\right)^{-2}= \frac{1}{7\cdot 7\cdot 7\cdot 7\cdot 7\cdot 7} \]

  112. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohhhh

  113. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    :DDD

  114. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    THANK YOUU

  115. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    btw I have a few more if you can help:?

  116. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    if you make a new post

  117. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i will!

  118. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.