Question

Помогите, пожалуйста!

Answer 1

$\dfrac{45^{n+1} }{3^{2n+1}\cdot5^{n-1}}= \dfrac{(5\cdot9)^{n+1} }{3^{2n+1}\cdot5^{n-1}}= \dfrac{(5\cdot3^{2} )^{n+1} }{3^{2n+1}\cdot5^{n-1}}= \dfrac{5^{n+1} \cdot3^{2n+2} }{3^{2n+1}\cdot5^{n-1}}=\\\\\\=3^{2n+2-2n-1}\cdot 5^{n+1-n+1} =3^{1} \cdot5^{2} =3\cdot25=\boxed{75}$