How to add numbers with same base but unknown exponents?












0












$begingroup$


I'm taking a university math course despite knowing better. Among the straightforward problems I encountered the following:



Simplify:



$$5^x +5^{x+2}$$



The answer is supposed to be $26*5^x$



How am I supposed to arrive at this conclusion, do I interpret this as some kind of short geometric sum?






algebra-precalculus exponentiation







share|cite|improve this question











$endgroup$

















    0












    $begingroup$


    I'm taking a university math course despite knowing better. Among the straightforward problems I encountered the following:



    Simplify:



    $$5^x +5^{x+2}$$



    The answer is supposed to be $26*5^x$



    How am I supposed to arrive at this conclusion, do I interpret this as some kind of short geometric sum?






    algebra-precalculus exponentiation







    share|cite|improve this question











    $endgroup$















      0












      0








      0





      $begingroup$


      I'm taking a university math course despite knowing better. Among the straightforward problems I encountered the following:



      Simplify:



      $$5^x +5^{x+2}$$



      The answer is supposed to be $26*5^x$



      How am I supposed to arrive at this conclusion, do I interpret this as some kind of short geometric sum?






      algebra-precalculus exponentiation







      share|cite|improve this question











      $endgroup$




      I'm taking a university math course despite knowing better. Among the straightforward problems I encountered the following:



      Simplify:



      $$5^x +5^{x+2}$$



      The answer is supposed to be $26*5^x$



      How am I supposed to arrive at this conclusion, do I interpret this as some kind of short geometric sum?






      algebra-precalculus exponentiation




      algebra-precalculus exponentiation






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 22 at 17:25









      pwerth

      3,265417




      3,265417










      asked Jan 22 at 17:17









      MagnusMagnus

      312313




      312313






















          1 Answer
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          9












          $begingroup$

          $5^{x}+5^{x+2}=5^{x}+5^{x}cdot 5^{2}=5^{x}(1+5^{2})=5^{x}cdot 26$






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            I didn't understand that last step, why can $5^x(1+5^2) $ be written as $5^x*26$?
            $endgroup$
            – Magnus
            Jan 22 at 17:22






          • 5




            $begingroup$
            Because $5^2=25$
            $endgroup$
            – Rhys Hughes
            Jan 22 at 17:23










          • $begingroup$
            ahh allright I guess I'm just tired today.
            $endgroup$
            – Magnus
            Jan 22 at 17:24











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          1 Answer
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          active

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          1 Answer
          1






          active

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          active

          oldest

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          active

          oldest

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          9












          $begingroup$

          $5^{x}+5^{x+2}=5^{x}+5^{x}cdot 5^{2}=5^{x}(1+5^{2})=5^{x}cdot 26$






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            I didn't understand that last step, why can $5^x(1+5^2) $ be written as $5^x*26$?
            $endgroup$
            – Magnus
            Jan 22 at 17:22






          • 5




            $begingroup$
            Because $5^2=25$
            $endgroup$
            – Rhys Hughes
            Jan 22 at 17:23










          • $begingroup$
            ahh allright I guess I'm just tired today.
            $endgroup$
            – Magnus
            Jan 22 at 17:24
















          9












          $begingroup$

          $5^{x}+5^{x+2}=5^{x}+5^{x}cdot 5^{2}=5^{x}(1+5^{2})=5^{x}cdot 26$






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            I didn't understand that last step, why can $5^x(1+5^2) $ be written as $5^x*26$?
            $endgroup$
            – Magnus
            Jan 22 at 17:22






          • 5




            $begingroup$
            Because $5^2=25$
            $endgroup$
            – Rhys Hughes
            Jan 22 at 17:23










          • $begingroup$
            ahh allright I guess I'm just tired today.
            $endgroup$
            – Magnus
            Jan 22 at 17:24














          9












          9








          9





          $begingroup$

          $5^{x}+5^{x+2}=5^{x}+5^{x}cdot 5^{2}=5^{x}(1+5^{2})=5^{x}cdot 26$






          share|cite|improve this answer









          $endgroup$



          $5^{x}+5^{x+2}=5^{x}+5^{x}cdot 5^{2}=5^{x}(1+5^{2})=5^{x}cdot 26$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 22 at 17:19









          pwerthpwerth

          3,265417




          3,265417












          • $begingroup$
            I didn't understand that last step, why can $5^x(1+5^2) $ be written as $5^x*26$?
            $endgroup$
            – Magnus
            Jan 22 at 17:22






          • 5




            $begingroup$
            Because $5^2=25$
            $endgroup$
            – Rhys Hughes
            Jan 22 at 17:23










          • $begingroup$
            ahh allright I guess I'm just tired today.
            $endgroup$
            – Magnus
            Jan 22 at 17:24


















          • $begingroup$
            I didn't understand that last step, why can $5^x(1+5^2) $ be written as $5^x*26$?
            $endgroup$
            – Magnus
            Jan 22 at 17:22






          • 5




            $begingroup$
            Because $5^2=25$
            $endgroup$
            – Rhys Hughes
            Jan 22 at 17:23










          • $begingroup$
            ahh allright I guess I'm just tired today.
            $endgroup$
            – Magnus
            Jan 22 at 17:24
















          $begingroup$
          I didn't understand that last step, why can $5^x(1+5^2) $ be written as $5^x*26$?
          $endgroup$
          – Magnus
          Jan 22 at 17:22




          $begingroup$
          I didn't understand that last step, why can $5^x(1+5^2) $ be written as $5^x*26$?
          $endgroup$
          – Magnus
          Jan 22 at 17:22




          5




          5




          $begingroup$
          Because $5^2=25$
          $endgroup$
          – Rhys Hughes
          Jan 22 at 17:23




          $begingroup$
          Because $5^2=25$
          $endgroup$
          – Rhys Hughes
          Jan 22 at 17:23












          $begingroup$
          ahh allright I guess I'm just tired today.
          $endgroup$
          – Magnus
          Jan 22 at 17:24




          $begingroup$
          ahh allright I guess I'm just tired today.
          $endgroup$
          – Magnus
          Jan 22 at 17:24


















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