anonymous
  • anonymous
What is the missing value? https://static.k12.com/bank_packages/files/media/mathml_6a898366c833b4d7194aa8d29fc91e60db252b97_1.gif A. −10 B. −2 C. 2 D. 10
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
jim_thompson5910
  • jim_thompson5910
hint: \[\LARGE \frac{x^a}{x^b} = x^{a-b}\]
anonymous
  • anonymous
D 10?

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jim_thompson5910
  • jim_thompson5910
\[\LARGE \frac{x^a}{x^b} = x^{a-b}\] \[\LARGE \frac{3^{-6}}{3^{{}^\boxed{}}} = 3^{4}\] \[\LARGE \frac{3^{-6}}{3^{x}} = 3^{4}\] \[\LARGE 3^{-6-x} = 3^{4}\] set the exponents equal to one another and solve for x
anonymous
  • anonymous
You lost me.
jim_thompson5910
  • jim_thompson5910
where at?
anonymous
  • anonymous
The last part
jim_thompson5910
  • jim_thompson5910
when I went from \[\LARGE \frac{3^{-6}}{3^{x}} = 3^{4}\] to \[\LARGE 3^{-6-x} = 3^{4}\] ???
anonymous
  • anonymous
Yes
jim_thompson5910
  • jim_thompson5910
I used that rule I wrote in the hint. When you divide expressions like x^3 over x^2, you subtract the exponents
anonymous
  • anonymous
Is it a? -10
jim_thompson5910
  • jim_thompson5910
solve -6 - x = 10 for x
jim_thompson5910
  • jim_thompson5910
sorry I meant -6 - x = 4
anonymous
  • anonymous
negative - a negative = a positive = -6 - (-2) = 4 Right?
jim_thompson5910
  • jim_thompson5910
-6 - (-2) = 4 is false
jim_thompson5910
  • jim_thompson5910
-6 - (-2) = -4 is true so try again
anonymous
  • anonymous
jim_thompson5910
  • jim_thompson5910
yes -6 - (-10) = -6 + 10 = 4
anonymous
  • anonymous
OKAY THANKS
jim_thompson5910
  • jim_thompson5910
no problem

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