document.write( "Question 1190689: What is z to the zero power times z to the negative 10th? Only using positive exponents. \n" ); document.write( "
Algebra.Com's Answer #822393 by Alan3354(69443)![]() ![]() You can put this solution on YOUR website! 0^0 = 1, by convention. \n" ); document.write( "======================== \n" ); document.write( "That means some people made that decision. \n" ); document.write( "------------------\r \n" ); document.write( "\n" ); document.write( "In 1752, Euler in Introductio in analysin infinitorum wrote that a0 = 1[15] and explicitly mentioned that 0^0 = 1.[16] An annotation attributed[17] to Mascheroni in a 1787 edition of Euler's book Institutiones calculi differentialis[18] offered the \"justification\"\r \n" ); document.write( "\n" ); document.write( "{\displaystyle 0^{0}=(a-a)^{n-n}={\frac {(a-a)^{n}}{(a-a)^{n}}}=1}{\displaystyle 0^{0}=(a-a)^{n-n}={\frac {(a-a)^{n}}{(a-a)^{n}}}=1} \n" ); document.write( "as well as another more involved justification. In the 1830s, Libri[19][17] published several further arguments attempting to justify the claim 0^0 = 1, though these were far from convincing, even by standards of rigor at the time.[20] \n" ); document.write( "--------------- \n" ); document.write( "I wouldn't argue with Euler. \n" ); document.write( " |