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anonymous

  • one year ago

Will fan and medal! Help please! Simplify. Express with positive exponents. Rationalize denominators. (a^(-4))/(a^(-2))

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  1. Owlcoffee
    • one year ago
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    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: \[A ^{-b}=\frac{ 1 }{ A^b }\]

  2. anonymous
    • one year ago
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    okay so it could just be (a^4)/(a^2)? @Owlcoffee

  3. Owlcoffee
    • one year ago
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    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.

  4. anonymous
    • one year ago
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    I really dont know how to simplify that @owlcoffee

  5. Owlcoffee
    • one year ago
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    When you deal with fractions inside a fraction you have to flip one and it turns into a multiplication: \[\frac{ \frac{ a }{ b } }{ \frac{ x }{ y } }=(\frac{ a }{ b })(\frac{ y }{ x })\]

  6. Owlcoffee
    • one year ago
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    Can you move on from here?

  7. anonymous
    • one year ago
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    okay well (A^-4)/(b^-2) *(a^4)/(b^2)??

  8. Owlcoffee
    • one year ago
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    Not quite.

  9. anonymous
    • one year ago
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    COuld you tell me what i did wrong?

  10. Owlcoffee
    • one year ago
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    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: \[\frac{ \frac{ 1 }{ a^4 } }{ \frac{ 1 }{ a^2 } }=(\frac{ 1 }{ a^4 })(\frac{ a^2 }{ 1 })\]

  11. anonymous
    • one year ago
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    1/a^2?

  12. Owlcoffee
    • one year ago
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    Correct, nice effort.!

  13. anonymous
    • one year ago
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    thank you! @Owlcoffee

  14. Owlcoffee
    • one year ago
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    No problem, thats why I am here.

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