Question

Simplifica : 2 la puterea 38 * 3 la puterea 40 +6 la puterea 38 -9 la puterea 19 *4 la puterea 20 , supra 3 la puterea 20 *4 la puterea 20-12 la puterea 19=

multumesc

Answer 1

Răspuns

Explicație pas cu pas:

$\frac{2^{38}\times 3^{40} + 6^{38}-9^{19}\times 4^{20}}{3^{20}\times 4^{20}-12^{19}} =$

$\frac{3^2\times (2\times3)^{38} + 6^{38}-3^{19\times2}\times 2^{20\times2}}{12^{20}-12^{19}} =$

$\frac{6\times (6)^{38} + 6^{38}-4\times3^{38}\times 2^{38}}{12^{19}(12-1)} =$

$\frac{6^{38}\times(6+1-4)}{12^{19}(11)} =\frac{6^{38}\times3}{12^{19}\times11} =\frac{6^{38}\times3}{6^{19}\times2^{19}\times11}=\frac{6^{19}\times3}{2^{19}\times11}=\frac{3^{19}\times3}{11}=\frac{3^{20}}{11}$