Question

40 баллов
Сократите дробь:
5²ⁿ⁺³×3ⁿ⁺⁵÷75ⁿ⁺²

Answer 1

$\frac{5^{2n + 3} * 3^{n + 5}}{75^{n + 2}} = \frac{5^{2n + 3} * 3^{n + 5}}{(5^2*3^1)^{n + 2}} = \frac{5^{2n + 3} * 3^{n + 5}}{5^{2(n+2)}* 3^{1(n+2)}}= \\ \\ = \frac{5^{2n + 3} * 3^{n + 5}}{5^{2n+4}*3^{n+2}}= 5^{2n+3-(2n+4)} * 3^{n+5-(n+2)} = \\ \\ =5^{2n+3-2n-4} * 3^{n+5-n-2} = 5^{-1}* 3^{3} = \frac{3^3}{5^1} = \\ \\ = \frac{27}{5} = 5.4$