Question

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

Answer 1

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

Answer 2

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