Question

Упростите 9^(n-1)/(3^n+3^(n-1))^2

Answer 1

$\frac{ 9^{n-1} }{ (3^n+ 3^{n-1} )^{2} } = \frac{9^n* 9^{-1} }{ 3^{2n} +2*3^n* 3^{n-1}+ 3^{2n-2} } =$
$\frac{9^n* \frac{1}{9} }{9^n+ \frac{2}{3}*9^n+ \frac{1}{9} *9^n } = \frac{9^n}{9*9^n+6*9^n+9^n} = \frac{1}{16 \\ }$