=> (27 : 9)ⁿ = 9²⁷ : 9²

=> 3ⁿ =  9²⁵

=> 3ⁿ = (3²)²⁵

=> 3ⁿ = 3⁵⁰

=> n = 50

3³ⁿ.3²ⁿ=3⁵⁴:3⁴

=>3⁵ⁿ=3⁵⁰

=>5n=50

=>n=10

a) \(3^{a+1}=81\)

\(3^{a+1}=3^4\)

\(a+1=4\)

\(a=3\)

b) \(\left(x-1\right)^3=27\)

\(\left(x-1\right)^3=3^3\)

\(x-1=3\)

\(x=4\)

\(a,3^{a+1}=81\\ \Rightarrow3^{a+1}=3^4\\ \\ \Rightarrow a+1=4\\ \Rightarrow a=3.\\ b,\left(x-1\right)^3=27\\ \Rightarrow\left(x-1\right)^3=3^3\\ \Rightarrow x-1=3\\ \Rightarrow x=4.\)

mk đã làm r nhé bn

\(27^n.9^n=9^{27}:81\)

\(3^{3n}.3^{2n}=3^{54}:3^4\)

\(3^{5n}=3^{50}\)

=> 5n = 50

=> n = 10

\(\frac{\left(-3\right)^n}{81}=-27\)

=> (-3)ⁿ = -27.81

=> (-3)ⁿ = -(27.81)

=> (-3)ⁿ = -(3³.3⁴)

=> (-3)ⁿ = -3⁷ = (-3)⁷

=> n = 7

Vậy n = 7

\(\frac{\left(-3\right)^n}{81}=-27\)

\(\left(-3\right)^n:81=-27\)

\(\left(-3\right)^n=-27\cdot81\)

\(\left(-3\right)^n=-2187\)

\(\left(-3\right)^n=\left(-3\right)^7\)

\(=>n=7\)

mk ghi lại đề nha:

27ⁿ : 9ⁿ = 9²⁷ : 81

(27 : 9)ⁿ = 9²⁷ : 9²

\(\Rightarrow\)     3ⁿ  = 9²⁵

\(\Rightarrow\)      3ⁿ = (3²)²⁵

\(\Rightarrow\)      3ⁿ  = 3⁵⁰

Vậy n = 50

\(27^n.9^n=9^{27}:81\Rightarrow3^{3n}:3^{2n}=3^{54}:3^4=3^{50}\)

\(\Rightarrow3^{5n}=3^{50}\Rightarrow5n=50\Rightarrow n=\frac{50}{5}=10\)

\(27^n.9^n=9^{27}:81\)

\(\left(27.9\right)^n=9^{27}:9^2\)

\(\left(27.9\right)^n=9^{25}\)

\(\left(3^3.3^2\right)^n=9^{25}\)

\(\left(3^5\right)^n=\left(3^2\right)^{25}\)

\(\left(3^5\right)^n=\left(3^5\right)^{10}\)

\(\Rightarrow n=10\)

a) n = 7 

b) n = 1 

a) \(\frac{\left(-3\right)^n}{81}=-27\)

\(\Rightarrow\left(-3\right)^n=-2187\)

\(\Rightarrow\left(-3\right)^n=\left(-3\right)^7\)

\(\Rightarrow n=7\)

Vậy \(n=7\)

b) \(8^n:2^n=4\)

\(8^n:2^n=4^1\)

mà \(8:2=4\)

\(\Rightarrow n=1\)

Vậy \(n=1\)