Justification of exponent laws

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How is the following operation justified? Specifically, what happens to the $4^n$ in the numerator. I tried looking online but could not determine how this was justified. Thanks.



$$dfrac(-3)^n-14^n= dfrac14cdot left(-dfrac34right)^n-1$$










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    up vote
    3
    down vote

    favorite












    How is the following operation justified? Specifically, what happens to the $4^n$ in the numerator. I tried looking online but could not determine how this was justified. Thanks.



    $$dfrac(-3)^n-14^n= dfrac14cdot left(-dfrac34right)^n-1$$










    share|cite|improve this question

























      up vote
      3
      down vote

      favorite









      up vote
      3
      down vote

      favorite











      How is the following operation justified? Specifically, what happens to the $4^n$ in the numerator. I tried looking online but could not determine how this was justified. Thanks.



      $$dfrac(-3)^n-14^n= dfrac14cdot left(-dfrac34right)^n-1$$










      share|cite|improve this question















      How is the following operation justified? Specifically, what happens to the $4^n$ in the numerator. I tried looking online but could not determine how this was justified. Thanks.



      $$dfrac(-3)^n-14^n= dfrac14cdot left(-dfrac34right)^n-1$$







      exponential-function






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      edited Apr 5 '15 at 22:02









      N. F. Taussig

      39.9k93253




      39.9k93253










      asked Apr 5 '15 at 20:26









      user3826764

      182




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          1 Answer
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          The $4^n$ is in the denominator.



          It becomes $4cdot 4^n-1$



          The $4^n-1$ is then combined with the $(-3)^n-1$ in the numerator.






          share|cite|improve this answer






















          • @N.F.Taussig: thank you for the $$ $
            – Henry
            Apr 5 '15 at 23:42










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          1 Answer
          1






          active

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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

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          active

          oldest

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          up vote
          0
          down vote



          accepted










          The $4^n$ is in the denominator.



          It becomes $4cdot 4^n-1$



          The $4^n-1$ is then combined with the $(-3)^n-1$ in the numerator.






          share|cite|improve this answer






















          • @N.F.Taussig: thank you for the $$ $
            – Henry
            Apr 5 '15 at 23:42














          up vote
          0
          down vote



          accepted










          The $4^n$ is in the denominator.



          It becomes $4cdot 4^n-1$



          The $4^n-1$ is then combined with the $(-3)^n-1$ in the numerator.






          share|cite|improve this answer






















          • @N.F.Taussig: thank you for the $$ $
            – Henry
            Apr 5 '15 at 23:42












          up vote
          0
          down vote



          accepted







          up vote
          0
          down vote



          accepted






          The $4^n$ is in the denominator.



          It becomes $4cdot 4^n-1$



          The $4^n-1$ is then combined with the $(-3)^n-1$ in the numerator.






          share|cite|improve this answer














          The $4^n$ is in the denominator.



          It becomes $4cdot 4^n-1$



          The $4^n-1$ is then combined with the $(-3)^n-1$ in the numerator.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Apr 5 '15 at 22:03









          N. F. Taussig

          39.9k93253




          39.9k93253










          answered Apr 5 '15 at 20:29









          Henry

          94.5k473150




          94.5k473150











          • @N.F.Taussig: thank you for the $$ $
            – Henry
            Apr 5 '15 at 23:42
















          • @N.F.Taussig: thank you for the $$ $
            – Henry
            Apr 5 '15 at 23:42















          @N.F.Taussig: thank you for the $$ $
          – Henry
          Apr 5 '15 at 23:42




          @N.F.Taussig: thank you for the $$ $
          – Henry
          Apr 5 '15 at 23:42

















           

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