<prompt> Nini thamani ya frac12times4timesfrac18times16timesfrac132times64timesfrac1128 mara256marafrac1512times1024?  <response>: Ninagundua kuwa kila neno katika bidhaa lina nguvu ya 2 au hali ya usawa. Kwa hivyo ninaweza kuandika bidhaa upya kama frac121times22timesfrac123times24timesfrac125 times26marafrac127time28marafrac129times210. Sasa naweza kutumia sheria kwamba fracamanam-n ili kurahisisha kila jozi ya masharti yanayofanana. Kwa mfano, frac121times2222-121. Vile vile, ninaweza kurahisisha jozi zingine kama frac1 23mara2421,frac125times2621,frac127times282 1,frac129times21021. Kwa hivyo bidhaa inakuwa 21times21times21times21times21 25. Kwa hiyo, thamani ya bidhaa ni 2532. 