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 2 days ago









      pwerth

      2,963416




      2,963416










      asked 2 days ago









      MagnusMagnus

      188213




      188213






















          1 Answer
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          8












          $begingroup$

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






          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
            2 days ago






          • 4




            $begingroup$
            Because $5^2=25$
            $endgroup$
            – Rhys Hughes
            2 days ago










          • $begingroup$
            ahh allright I guess I'm just tired today.
            $endgroup$
            – Magnus
            2 days ago











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          1 Answer
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          active

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          1 Answer
          1






          active

          oldest

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          active

          oldest

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          active

          oldest

          votes









          8












          $begingroup$

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






          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
            2 days ago






          • 4




            $begingroup$
            Because $5^2=25$
            $endgroup$
            – Rhys Hughes
            2 days ago










          • $begingroup$
            ahh allright I guess I'm just tired today.
            $endgroup$
            – Magnus
            2 days ago
















          8












          $begingroup$

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






          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
            2 days ago






          • 4




            $begingroup$
            Because $5^2=25$
            $endgroup$
            – Rhys Hughes
            2 days ago










          • $begingroup$
            ahh allright I guess I'm just tired today.
            $endgroup$
            – Magnus
            2 days ago














          8












          8








          8





          $begingroup$

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






          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 2 days ago









          pwerthpwerth

          2,963416




          2,963416












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






          • 4




            $begingroup$
            Because $5^2=25$
            $endgroup$
            – Rhys Hughes
            2 days ago










          • $begingroup$
            ahh allright I guess I'm just tired today.
            $endgroup$
            – Magnus
            2 days ago


















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






          • 4




            $begingroup$
            Because $5^2=25$
            $endgroup$
            – Rhys Hughes
            2 days ago










          • $begingroup$
            ahh allright I guess I'm just tired today.
            $endgroup$
            – Magnus
            2 days ago
















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




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




          4




          4




          $begingroup$
          Because $5^2=25$
          $endgroup$
          – Rhys Hughes
          2 days ago




          $begingroup$
          Because $5^2=25$
          $endgroup$
          – Rhys Hughes
          2 days ago












          $begingroup$
          ahh allright I guess I'm just tired today.
          $endgroup$
          – Magnus
          2 days ago




          $begingroup$
          ahh allright I guess I'm just tired today.
          $endgroup$
          – Magnus
          2 days ago


















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