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anonymous

  • one year ago

What is the missing exponent? [ ] (2^-5) =2^-15 The missing exponent is in the brackets, I just need help finding it.

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  1. anonymous
    • one year ago
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    After this one, I have one more question if your willing to help out.

  2. Jhannybean
    • one year ago
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    Say the missing exponent = x. Then... \[(2^{-5}) (x) = 2^{-15}\] we can find x by dividing the two given exponents. \(\dfrac{2^{-15}}{2^{-5}}\) When dividing exponents, the powers subtract eachother. \(\dfrac{x^m}{x^{n}} = x^{m-n}\)

  3. Jhannybean
    • one year ago
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    Do you see what I mean?

  4. anonymous
    • one year ago
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    Sort of

  5. anonymous
    • one year ago
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    Yea ok, I get it now

  6. Jhannybean
    • one year ago
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    What did yu get as the missing exponent?

  7. Jhannybean
    • one year ago
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    Okay. Lets solve for \(\dfrac{2^{-15}}{2^{-5}}\) first. What is \(2^{-15+5} =~?\)

  8. anonymous
    • one year ago
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    2^-10 also, how do you get the power of numbers without the ^

  9. Jhannybean
    • one year ago
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    -15 + 5 = -20??

  10. Jhannybean
    • one year ago
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    Yes, you are right, it is -5, but remember our rule? \(\large \dfrac{2^{-15}}{2^{-5}} = 2^{-15 -(-5)}= 2^{-15 + 5}\)

  11. anonymous
    • one year ago
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    oh yea, so it is 2^-10 ok

  12. Jhannybean
    • one year ago
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    Remember, 2 negatives make a positive :D

  13. Jhannybean
    • one year ago
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    Mmhmm, it's 2\(^{-10}\)

  14. Jhannybean
    • one year ago
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    So do you agree that if \(x=2^{-10}\), that \((2^{-5})(2^{-10}) = 2^{-15}\)?

  15. anonymous
    • one year ago
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    Yes, so then in the blank, I would put 2^-10

  16. Jhannybean
    • one year ago
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    Yes :D \(\checkmark\)

  17. anonymous
    • one year ago
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    thanks

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