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

\(\left(-3\right)^n=-2187=\left(-3\right)^7\)

=> n = 7

Chúc bạn học tốt nha!!!

ta có: \(\left(\frac{1}{81}\right)=\left(\frac{1}{3}\right)^4\) 

=>n=4

(1/3)^n = 1/81 = (1/3) ^4

=> n = 4

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\(\left(\frac{1}{3}\right)^n=\frac{1}{81}\)

\(\Leftrightarrow\left(\frac{1}{3}\right)^n=\left(\frac{1}{3}\right)^4\)

\(\Leftrightarrow n=4\)

27^n:3^n=9

3^3n:3^n=3^2

3^(3n-n)=3^2

suy ra 3n-n=2

n(3-1)=2

n.2=2

Vậy n=2:2

n=1

còn câu sau cậu tự tính

\(n=1\)

\(27^n:3^n=9\)

Khi n = 1

<=> \(\frac{3^{3n}}{3^n}=9\)<=> \(3^{2n}=3^2\)<=>n=1

\(27^n\div3^n=9\)

\(\Rightarrow3^{3n}\div3^n=9\)

\(\Rightarrow3^{3n-n}=9\)

\(\Rightarrow3^{2n}=3^2\)

\(\Rightarrow2n=2\)

\(\Leftrightarrow n=1\)

Vậy muốn 27^n : 3^n = 9 thì n=1

ta có:

\(27^n:3^n=9\)

\(=>\left(27:3\right)^n=9\)

\(=>9^n=9\)

\(=>n=1\)

hoặc:\(n:n=1\)

\(27:9:1=3\)

Ta có:

\(27^n:3^n=9\)

Vì \(27:3=9\)

\(\Leftrightarrow n=1\)

\(a,\frac{16}{2^n}=2=>\frac{2^4}{2^n}=2=>2^4:2^n=2=>2^{4-n}=2=>4-n=1=>n=3\)

\(b,\frac{\left(-3\right)^n}{81}=-27=>\frac{\left(-3\right)^n}{3^4}=\left(-3\right)^3=>\frac{\left(-3\right)^n}{\left(-3\right)^4}=\left(-3\right)^3=>\left(-3\right)^{n-4}=\left(-3\right)^3=>n-4=3=>n=7\)

\(c,8^n:2^n=4=>\left(8:2\right)^n=4=>4^n=4=>n=1\)

\(a,\frac{1}{27}\times81^n=3^n\)

\(\frac{1}{3^3}\times\left(3^4\right)^n=3^n\)

\(\frac{3^{4\times n}}{3^3}=3^n\)

\(3=3^n\)

\(\Rightarrow n=1\)