Question

a theory of indices question :
3^2n 27^-n *81^n /9^n+1 =

Answer 1

$\frac{3^{2n}\ 27^{-n}\ 81^n}{9^{n+1}}=\frac{3^{2n}\ (3^3)^{-n}\ (3^4)^n}{(3^3)^{n+1}}\\\\=\frac{3^{2n}\ 3^{-3n}\ 3^{4n}}{3^{3n+3}}\\\\=3^{2n-3n+4n-3n-3}=3^{-3}=\frac{1}{3^3}=\frac{1}{27}$