Question

Сократите дробь 50(степень n+1)/2(степень n-3)*5(степень 2n+1) и объянение,

Answer 1

50^n+1 / 2^n-3 * 5^2n+1 = (25*2)^n+1 / 2^n-3 * 5^2n+1 = 25^n+1 * 2^n+1 / 2^n-3 * 5^2n+1 =

=(5^2)^n+1 * 2^n+1 / 2^n-3 * 5^2n+1= 5^2(n+1) * 2^n+1 / 2^n-3 * 5^2n+1 = 5^2n+1 * 2^n+1 / 2^n-3 * 5^2n+1 = 5^ 2n+2-(2n+1) * 2^n+1-(n-3) = 5^1 * 2^4=5*16=80

Answer 2

$\frac{50^{n+1}}{2^{n-3}*5^{2n+1}}=\frac{50*(5^2*2)^{n}}{2^{-3}*2^n*5*5^{2n}}=$

$=\frac{50*8*5^{2n}*2^{n}}{5*2^n*5^{2n}}=\frac{50*8}{5}=10*8=80$