anonymous
  • anonymous
Will fan and medal! Help please! Simplify. Express with positive exponents. Rationalize denominators. (a^(-4))/(a^(-2))
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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Owlcoffee
  • Owlcoffee
There's an interesting property of exponential expressions that allows us to express any negative exponent as a positive. That is: doing the reciprocate, or more visually: \[A ^{-b}=\frac{ 1 }{ A^b }\]
anonymous
  • anonymous
okay so it could just be (a^4)/(a^2)? @Owlcoffee
Owlcoffee
  • Owlcoffee
That's not correct, if we apply it: \[\frac{ a ^{-4} }{ a ^{-2} }\] Will turn into: \[\frac{ \frac{ 1 }{ a^4 } }{ \frac{ 1 }{ a^2 } }\] So all you have to do is simplify that.

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anonymous
  • anonymous
I really dont know how to simplify that @owlcoffee
Owlcoffee
  • Owlcoffee
When you deal with fractions inside a fraction you have to flip one and it turns into a multiplication: \[\frac{ \frac{ a }{ b } }{ \frac{ x }{ y } }=(\frac{ a }{ b })(\frac{ y }{ x })\]
Owlcoffee
  • Owlcoffee
Can you move on from here?
anonymous
  • anonymous
okay well (A^-4)/(b^-2) *(a^4)/(b^2)??
Owlcoffee
  • Owlcoffee
Not quite.
anonymous
  • anonymous
COuld you tell me what i did wrong?
Owlcoffee
  • Owlcoffee
Yes, when we make them into: \[\frac{ a ^{-4} }{ a ^{-2} }=\frac{ \frac{ 1 }{ a^4 } }{ \frac{ 1 }{ a^2 } }\] We already got rid of the negative expressions, so we will only focus n the right side of the expression I wrote you above, more clearly: \[\frac{ \frac{ 1 }{ a^4 } }{ \frac{ 1 }{ a^2 } }\] And we can simplify it using the property I stated to you earlier: \[\frac{ \frac{ 1 }{ a^4 } }{ \frac{ 1 }{ a^2 } }=(\frac{ 1 }{ a^4 })(\frac{ a^2 }{ 1 })\]
anonymous
  • anonymous
1/a^2?
Owlcoffee
  • Owlcoffee
Correct, nice effort.!
anonymous
  • anonymous
thank you! @Owlcoffee
Owlcoffee
  • Owlcoffee
No problem, thats why I am here.

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