Question

Упростите выражение 18*12^3n-1 дробная черта 9^2n+1 *2^4n-3

Answer 1

$frac{18cdot12^{3n-1}}{9^{2n+1}cdot2^{4n-3}} =frac{2cdot 3^2cdot3^{3n-1}cdot2^{6n-2}}{3^{4n+2}cdot2^{4n-3}} =2^{1+6n-2-4n+3}cdot3^{2+3n-1-4n-2}=2^{2n+2}cdot3^{-n-1}=frac{2^{2n+2}}{3^{n+1}}$

Answer 2

$frac{18*12^{3n-1}}{9^{2n+1}*2^{4n-3}}=frac{2*3^2*2^{6n-2}*3^{3n-1}}{3^{4n+2}*2^{4n-3}}= \ \ =2^{1+6n-2-(4n-3)}*3^{2+3n-1-(4n+2)}= \ \ = 2^{1+6n-2-4n+3}*3^{2+3n-1-4n-2}=2^{2n+2}*3^{-n-1}= \ \ = 2^{2(n+1)}*3^{-(n+1)}=frac{(2^2)^{n+1}}{3^{n+1}}= frac{4^{n+1}}{3^{n+1}}=(frac{4}{3})^{n+1}$