anonymous
  • anonymous
How to evaluate -> (5^-4 - 5^-6)/(5^-3 +5^-5)
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
bet you got the idea now. write it without the negative exponents. then clear the fractions
anonymous
  • anonymous
Okay so:
anonymous
  • anonymous
\[\frac{5^{-4} - 5^{-6}}{5^{-3} +5^{-5}}\] muttiply top and bottom by \[5^6\]

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anonymous
  • anonymous
I got (1/5^4 - 1/5^6)/ (1/5^3 +1/5^5)
anonymous
  • anonymous
wait. How come I have to multiply top and bottom by 5^6?
anonymous
  • anonymous
that will clear the fractions. \[5^{-4}\times 5^6=5^2\]
anonymous
  • anonymous
if you want you can write this in fraction notation. then you will see that you should multiply top and bottom by \[5^6\]
anonymous
  • anonymous
i will write it out if you like
anonymous
  • anonymous
please do, thanks
anonymous
  • anonymous
\[\frac{5^{-4}-5^{-6}}{5^{-3}+5^{-5}}\times \frac{5^6}{5^6}\]
anonymous
  • anonymous
\[\frac{5^2-1}{5^3+5}\] is the second line clear?
anonymous
  • anonymous
pardon?
anonymous
  • anonymous
i added the exponents, and i chose \[5^6\] so that they would all be positive
anonymous
  • anonymous
okay
anonymous
  • anonymous
because i want to evaluate the numbers, i need the exponents to be positive
anonymous
  • anonymous
mmhm
anonymous
  • anonymous
now i can see what the numbers are. numerator is 25+1=26
anonymous
  • anonymous
denominator is 125+5=130
anonymous
  • anonymous
Isn't the numerator 25-1?
anonymous
  • anonymous
oops yes
anonymous
  • anonymous
Okay, that's great, thanks :) I was making it way more complicated thn it needed to be
anonymous
  • anonymous
i would like to say that was a "typo" but i guess it was a mistake. in any case you have the answer, it is \[\frac{24}{130}=\frac{12}{65}\]
anonymous
  • anonymous
good! yw
anonymous
  • anonymous
i like ur pic

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