Question

√2 la puterea1×2 la a doua×2la a treia×.......×2 la 40

Answer 1

$\sqrt{ 2^{1}* 2^{2}*...* 2^{40} } = \sqrt{2^{1+2+...+40} }= \sqrt{ 2^{40*41:2} }= \sqrt{ 2^{820} }= \sqrt{ {(2^{410})}^{2} } =$$= 2^{410}.$ S-a folosit regula inmultirii puterilor cu aceeasi baza si suma lui Gauss.

Answer 2

     
$\sqrt{ 2^{1}*2^{2}*2^{3}*...*2^{40}}= \\ \\ =\sqrt{ 2^{1+2+3+....+40}}= \\ \\ = \sqrt{ 2^{ \frac{40*41}{2}}}= \\ \\ =\sqrt{ 2^{20*41}}= \sqrt{ 2^{820}} = 2^{410}$