Question

упростите выражение
$\frac{36 {}^{n + 1} }{3 {}^{2n + 1} \times 4 {}^{n - 2} }$
пожалуйста помогите ​

Answer 1

(a^n)^m = a^(nm)

a^m*b^m = (ab)^m

^ степень

36^(n+1) = (6^2)^(n + 1) = (2*3)^(2n + 2) = 2^(2n+2)*3^(2n+2)

4^(n-2) = (2^2)^(n - 2) = 2^2(n-2) = 2^(2n - 4)

36^(n+1)/3^(2n+1)*4(n-2) = 2^(2n+2)*3^(2n+2)/3^(2n+1)*2^(2n-4) =

2^(2n+2 - 2n + 4) *3^(2n+2-2n - 1) = 2^6*3 = 64*3 = 192