Question

$2^{1}$·$2^{2}$·$2^{3}$ ·....·$2^{100}$

Answer 1

$n^a*n^b=n^{a+b}$
$2^1*2^2*2^3*...*2^{100}=2^{1+2+3+...+100}$
$1+2+3+...+n= \frac{n(n+1)}{2}$
$1+2+3+...+100= \frac{100(100+1)}{2} =50(100+1)=5000+50=5050$
$2^1*2^2*2^3*...*2^{100}=2^{1+2+3+...+100}=2^{5050}$