anonymous
  • anonymous
What is the missing exponent? [ ] (2^-5) =2^-15 The missing exponent is in the brackets, I just need help finding it.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
After this one, I have one more question if your willing to help out.
Jhannybean
  • Jhannybean
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. \(\dfrac{x^m}{x^{n}} = x^{m-n}\)
Jhannybean
  • Jhannybean
Do you see what I mean?

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anonymous
  • anonymous
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anonymous
  • anonymous
Yea ok, I get it now
Jhannybean
  • Jhannybean
What did yu get as the missing exponent?
Jhannybean
  • Jhannybean
Okay. Lets solve for \(\dfrac{2^{-15}}{2^{-5}}\) first. What is \(2^{-15+5} =~?\)
anonymous
  • anonymous
2^-10 also, how do you get the power of numbers without the ^
Jhannybean
  • Jhannybean
-15 + 5 = -20??
Jhannybean
  • Jhannybean
Yes, you are right, it is -5, but remember our rule? \(\large \dfrac{2^{-15}}{2^{-5}} = 2^{-15 -(-5)}= 2^{-15 + 5}\)
anonymous
  • anonymous
oh yea, so it is 2^-10 ok
Jhannybean
  • Jhannybean
Remember, 2 negatives make a positive :D
Jhannybean
  • Jhannybean
Mmhmm, it's 2\(^{-10}\)
Jhannybean
  • Jhannybean
So do you agree that if \(x=2^{-10}\), that \((2^{-5})(2^{-10}) = 2^{-15}\)?
anonymous
  • anonymous
Yes, so then in the blank, I would put 2^-10
Jhannybean
  • Jhannybean
Yes :D \(\checkmark\)
anonymous
  • anonymous
thanks

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