Question

Va rog frumosss ajutatima dau coriana.Compara nr c) 2•2 la puterea 2 • 2 la puterea 3• ........•2 la putere 10 si 3 la puterea 44

Answer 1

2 × 2^2 × 2^3 ×...×2^10 =

= 2^(1+2+3+...+10) =

= 2^10×11:2 =

= 2^5×11 =

= 2^55

2^55 =( 2^5)^11 = 32^11
3^44 = (3^4)^11 = 81^11

32^11 < 81^11

deci: 2^55 < 3^44

Answer 2

2·2²·2³·2⁴.....·2¹⁰=
=2⁽¹⁺²⁺³⁺⁴⁺ ⁺¹⁰⁾
= 2^{10*11:2}
=2⁵⁵
=2⁵⁾¹¹
=32¹¹
3⁴⁴=3⁴⁾¹¹=81¹¹

32¹¹ < 81¹¹