Question

son con evidencias gracias

Answer 1

1) Reduce:

$\frac{3^{n+8}\cdot \:0.3^{n+9}}{3^{n+6}\cdot \:0.3^{n+10}}$

$\frac{3^{n+8}}{3^{n+6}}=3^{\left(n+8\right)-\left(n+6\right)}=3^2$

$=\frac{3^2\cdot \:0.3^{n+9}}{0.3^{n+10}}$

$\frac{0.3^{n+9}}{0.3^{n+10}}=\frac{1}{0.3^{\left(n+10\right)-\left(n+9\right)}}=\frac{1}{0.3}$

$=\frac{3^2}{0.3}$

$3^2=9$

$=\frac{9}{0.3}$

$=30$

2) Calcular el valor de A:

$A=\frac{5^{2n+4}\cdot \:0.5^{3n+1}\cdot \:0.5^{4n+1}}{5^{7n+1}\cdot \:0.5^{2n+4}}$

$5^{2n+4}\cdot \:0.5^{3n+1}\cdot \:0.5^{4n+1}=5^{2n+4}\cdot \:0.5^{7n+2}$

$A=\frac{5^{2n+4}\cdot \:0.5^{7n+2}}{5^{7n+1}\cdot \:0.5^{2n+4}}$

$\frac{5^{2n+4}}{5^{7n+1}}=5^{\left(2n+4\right)-\left(7n+1\right)}=5^{-5n+3}$

$A=\frac{5^{-5n+3}\cdot \:0.5^{7n+2}}{0.5^{2n+4}}$

$\frac{0.5^{7n+2}}{0.5^{2n+4}}=0.5^{\left(7n+2\right)-\left(2n+4\right)}=0.5^{5n-2}$

$A=5^{-5n+3}\cdot \:0.5^{5n-2}$

¡Espero haberte ayudado GabrielaChampi!