упростите выражение
[tex] \frac{36 {}^{n + 1} }{3 {}^{2n + 1} \times 4 {}^{n - 2} } [/tex]
пожалуйста помогите
[tex] \frac{36 {}^{n + 1} }{3 {}^{2n + 1} \times 4 {}^{n - 2} } [/tex]
пожалуйста помогите
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Verified answer
(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