Question

simplificati urmatoarea fractie pana obtineti fractie ireductibila:
2 la puterea 101 x 3 la puterea 100 +2 la puterea 100x 3 la puterea 101 + 6 la puterea 101 totul  supra 2 la puterea 101 x 3 la puterea 102 +5 x 6 la puterea 101

Answer 1

         
$\frac{ 2^{101}* 3^{100}+2^{100}*3^{101} + 6^{101}}{ 2^{101}*3^{102}+5* 6^{101}}= \\ \\ =\frac{ 2*(2^{100}* 3^{100})+3*(2^{100}*3^{100}) + 6*(6^{100})}{ 2* 3^{2}*(2^{100}*3^{100})+5*6*(6^{100})}= \\ \\ = \frac{ 2(6^{100})+3*(6^{100}) + 6*(6^{100})}{ 2* 3^{2}*(6^{100})+5*6*(6^{100})}= \\ \\ = \frac{ (6^{100})(2+3 + 6)}{ (6^{100})( 2* 3^{2}+5*6 )}= \frac{2+3 + 6}{ 2* 3^{2}+5*6 }= \frac{5 + 6}{ 2* 9+5*6 }= \frac{11}{ 18+30 }= \boxed {\frac{11}{48}}$