a) 27^n : 3^n = 9

     (27 : 3)^n  = 9

         9^n        = 9

=> n = 1

b) 25/5^n = 5

       5^n     = 25 : 5

       5^n     = 5

=> n = 1

c) 81/(-3)^n = -243

         (-3)^n   = -243 : 81

         (-3)^n   = -3

=> n = 1

d) 1/2 . 2^n + 4 . 2^n = 9 . 2^5

       2^n . (1/2 + 4)     = 9 . 32

       2^n . 9/2              = 288

       2^n                       = 288 : 9/2

       2^n                       = 64

       2^n                       = 2^6

=> n = 6

thank you for doing your homework well !

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

\(9^n=9\rightarrow n=1\)

\(\left(\frac{25}{5}\right)^n=5^n=5^1\)

\(\rightarrow n=1\)

\(\frac{81}{\left(-3\right)^n}=-243=\left(-3\right)^5\)

\(\rightarrow\left(-3\right)^n=81:\left(-3\right)^5=\frac{-1}{3}=\left(-3\right)^{-1}\)

\(\)

a) \(3^3\)

b)\(2^8\)

c) \(2^7\)

d) \(3^1\)

a) 9.3³.\(\dfrac{1}{81}\) .3² = 3². 3³.\(\dfrac{1}{3^4}\) . 3² = 3³

b) 4. 2⁵: \(\) (2³.\(\dfrac{1}{16}\))= 2². 2⁵: 2³. \(\dfrac{1}{2^4}\) = 2⁷: \(\dfrac{1}{2}\) = 2⁷. 2= 2⁸

c) 3². 2⁵. \(\left(\dfrac{2}{3}\right)^2\) = 3². 2⁵. \(\dfrac{2^2}{3^2}\) = 2⁵. 2² = 2⁷

d) \(\left(\dfrac{1}{3}\right)^2\) .\(\dfrac{1}{3}\) . 9² = \(\dfrac{1}{9}.\dfrac{1}{3}\). 9² = \(\dfrac{9}{3}\) = 3¹

a,Ta có \(\left(3^3\right)^n:3^n=9\Leftrightarrow3^{3n}:3^n=3^2\Leftrightarrow3n-n=2\Leftrightarrow n=1\)

b,TA có \(\dfrac{5^2}{5^n}=5^1\Leftrightarrow2-n=1\Leftrightarrow n=1\)

Các câu sau để bn tự làm

a) 27ⁿ : 3ⁿ = 9

\(\Leftrightarrow\) (27 : 3)ⁿ = 9

\(\Leftrightarrow\) 9ⁿ = 9

\(\Leftrightarrow\) n = 1

b) \(\dfrac{25}{5^n}=5\)

\(\Leftrightarrow\dfrac{5^2}{5^n}=5\)

\(\Leftrightarrow5^n.5=5^2\)

\(\Leftrightarrow5^{n+1}=5^2\)

\(\Leftrightarrow n+1=2\)

n = 2 - 1

n = 1

c) \(\dfrac{81}{\left(-3\right)^n}=-243\)

\(\Leftrightarrow\dfrac{\left(-3\right)^4}{\left(-3\right)^n}=\left(-3\right)^5\)

\(\Leftrightarrow\left(-3\right)^n.\left(-3\right)^5=\left(-3\right)^4\)

\(\Leftrightarrow\left(-3\right)^{n+5}=\left(-3\right)^4\)

\(\Leftrightarrow n+5=4\)

n = 4 - 5

n = -1

a)\(\dfrac{1}{9}.27^n=3^n\)

<=>27ⁿ=3ⁿ:\(\dfrac{1}{9}\)

<=>27ⁿ:3ⁿ=\(\dfrac{1}{9}\)

<=>3³ⁿ:3ⁿ=\(\dfrac{1}{9}\)

<=>3²ⁿ=\(\dfrac{1}{9}\)

<=>9ⁿ=\(\dfrac{1}{9}\)

<=>9ⁿ⁺¹=1

<=>n+1=0

<=>n=-1

vậy n=-1

a)n=1

b)n=4

c)n=1

d)n=6

e)n=-1

cái này mà bạn ko biết làm á, bấm máy tính tạch tạch mấy phát là ra mà

lười làm nên nhờ mấy bạn giải dùm

a) \(2^{-1}\cdot2^n+4\cdot2^n=9\cdot2^5\)

\(\Rightarrow2^n\cdot\left(2^{-1}+4\right)=9\cdot2^5\)

\(\Rightarrow2^n\cdot4,5=288\)

\(\Rightarrow2^n=64\)

\(\Rightarrow n=6\)

b) \(2^m-2^n=1984\)

\(\Rightarrow2^n\cdot\left(2^{m-n}-1\right)=2^6\cdot31\)

\(\Rightarrow\left\{{}\begin{matrix}2^n=2^6\\2^{m-n}-1=31\end{matrix}\right.\)

\(\Rightarrow n=6\)

\(\Rightarrow2^{m-n}=32\Rightarrow m-n=5\Rightarrow m=11\)

1.

\(\left(\dfrac{-2}{3}\right).0,75+1\dfrac{2}{3}:\left(\dfrac{-4}{9}\right)+\left(\dfrac{-1}{2}\right)^2\)

\(=\left(\dfrac{-2}{3}\right).\dfrac{3}{4}+\dfrac{5}{3}.\left(\dfrac{9}{-4}\right)+\dfrac{1}{4}\)

\(=-\dfrac{1}{2}+\dfrac{45}{-12}+\dfrac{1}{4}\)

\(=-\dfrac{6}{12}+\dfrac{-45}{12}+\dfrac{3}{4}\)

\(=\dfrac{-48}{12}\)

\(=-4\)

2.

a) \(\dfrac{3}{4}-\left(x+\dfrac{1}{2}\right)=\dfrac{4}{5}\)

\(\Leftrightarrow x+\dfrac{1}{2}=\dfrac{3}{4}-\dfrac{4}{5}\)

\(\Leftrightarrow x+\dfrac{1}{2}=\dfrac{-1}{20}\)

\(\Leftrightarrow x=\dfrac{-1}{20}-\dfrac{1}{2}\)

\(\Leftrightarrow x=\dfrac{-1}{20}-\dfrac{10}{20}\)

\(\Leftrightarrow x=\dfrac{-11}{20}\)

b) \(\left|x-\dfrac{2}{5}\right|+\dfrac{3}{4}=\dfrac{11}{4}\)

\(\Leftrightarrow\left|x-\dfrac{2}{5}\right|=\dfrac{11}{4}-\dfrac{3}{4}\)

\(\Leftrightarrow\left|x-\dfrac{2}{5}\right|=2\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{2}{5}=-2\Rightarrow x=-2+\dfrac{2}{5}=\dfrac{-8}{5}\\x-\dfrac{2}{5}=2\Rightarrow x=2+\dfrac{2}{5}=\dfrac{12}{5}\end{matrix}\right.\)

3.

a) \(\dfrac{16}{2^n}=2\)

\(\Leftrightarrow2^n=16:2\)

\(\Leftrightarrow2^n=8\)

\(\Leftrightarrow2^n=2^3\)

\(\Leftrightarrow n=3\)

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

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

\(\Leftrightarrow\left(-3\right)^n=\left(-3\right)^3.\left(-3\right)^4\)

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

\(\Leftrightarrow n=7\)

4. Ta có:

\(\dfrac{x}{2}=\dfrac{y}{3}\Rightarrow\dfrac{x}{10}=\dfrac{y}{15}\) (1)

\(\dfrac{y}{5}=\dfrac{z}{4}\Rightarrow\dfrac{y}{15}=\dfrac{z}{12}\) (2)

Từ (1) và (2) suy ra \(\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{12}\)

Vì \(x-y+x=-49\) ta có:

\(\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{12}=\dfrac{x-y+z}{10-15+12}=\dfrac{-49}{7}=-7\)

Vậy \(\left\{{}\begin{matrix}x=\left(-7\right).10=-70\\y=\left(-7\right).15=-105\\z=\left(-7\right).12=-84\end{matrix}\right.\)