a) \(\left(2x+3\right)^2=\frac{9}{144}\)

\(\Leftrightarrow\left(2x+3\right)^2=\left(\frac{1}{4}\right)^2=\left(-\frac{1}{4}\right)^2\)

\(\Rightarrow\orbr{\begin{cases}2x+3=\frac{1}{4}\\2x+3=\frac{-1}{4}\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=\frac{-11}{4}\\2x=\frac{-13}{4}\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{-11}{8}\\x=\frac{-13}{8}\end{cases}}}\)

Vậy ...

b) Ta có: \(\left(3x-1\right)^3=\frac{-8}{27}=\left(\frac{-2}{3}\right)^3\)

\(\Leftrightarrow3x-1=\frac{-2}{3}\Leftrightarrow3x=\frac{1}{3}\Leftrightarrow x=\frac{1}{9}\)

Vậy ....

c) \(x^{10}=25x^8\Leftrightarrow x^{10}:x^8=25\Leftrightarrow x^2=25\Leftrightarrow x=\left\{5;-5\right\}\)

Vậy ...

d) \(\frac{x^7}{81}=27\Leftrightarrow x^7=27.81=2187\)

Mà 3⁷ = 2187 => x⁷ = 3⁷ => x = 3

Vậy ....

e) \(\frac{x^8}{9}=729\Leftrightarrow x^8=729.9=6561\)

Mà 3⁸ = (-3)⁸ = 6561

=> x⁸ = 3⁸ = (-3)⁸

=> x = {-3;3}

Vậy ...

a) \(\frac{x^7}{81}=27\)

=> x⁷ = 27.81

=> x⁷ = 3³.3⁴

=> x⁷ = 3⁷

=> x = 3

Vậy x = 3

b) \(\frac{x^8}{9}=729\)

=> x⁸ = 729.9

=> x⁸ = 3⁶.3²

=> x⁸ = 3⁸ = (-3)⁸

=> \(x\in\left\{3;-3\right\}\)

Vậy \(x\in\left\{3;-3\right\}\)

a)

\(\begin{array}{l}x - \left( { - \frac{7}{9}} \right) =  - \frac{5}{6}\\x + \frac{7}{9} =  - \frac{5}{6}\\x =  - \frac{5}{6} - \frac{7}{9}\\x =  - \frac{{15}}{{18}} - \frac{{14}}{{18}}\\x = \frac{{ - 29}}{{18}}\end{array}\)

Vậy \(x = \frac{{ - 29}}{{18}}\).

b)

\(\begin{array}{l}\frac{{15}}{{ - 4}} - x = 0,3\\x = \frac{{15}}{{ - 4}} - 0,3\\x =  - 3,75 - 0,3\\x =  - 4,05\end{array}\)

Vậy \(x =  - 4,05\).

x^7/81 = 27                                                    x^8/9 = 729

x^7 : 81= 27                                                   x^8  : 9 = 729

x^7       =27.81                                                x^8       = 729.9

x^7        =2187                                                x^8       =6561

x^7        = 3^7                                                  x^8       = 3^8

=> x      =3                                                       => x      = 3

\(\frac{x^7}{81}=27\Rightarrow x^7=27.81=2187\Rightarrow x=\sqrt[7]{2187}=3\)

\(\frac{x^8}{9}=729\Rightarrow x^8=729.9=6561\Rightarrow x=\sqrt[8]{6561}=3\)

\(\frac{x^7}{81}=27\)

\(\Rightarrow x^7.1=81.27\)

\(\Rightarrow x^7=2187\)

Ta thấy : \(3^7=2187\)

\(\Rightarrow x=\sqrt[7]{2187}=3\)

\(\frac{x^8}{9}=729\)

\(\Rightarrow x^8.1=729.9\)

\(\Rightarrow x^8=6561\)

\(\Rightarrow x=\sqrt[8]{6561}=3\)

a)

\(\begin{array}{l}x.\frac{{14}}{{27}} = \frac{{ - 7}}{9}\\x = \frac{{ - 7}}{9}:\frac{{14}}{{27}}\\x = \frac{{ - 7}}{9}.\frac{{27}}{{14}}\\x = \frac{{ - 3}}{2}\end{array}\)                

Vậy \(x = \frac{{ - 3}}{2}\).

b)

\(\begin{array}{l}\left( {\frac{{ - 5}}{9}} \right):x = \frac{2}{3}\\x = \left( {\frac{{ - 5}}{9}} \right):\frac{2}{3}\\x = \left( {\frac{{ - 5}}{9}} \right).\frac{3}{2}\\x = \frac{{ - 5}}{6}\end{array}\)

Vậy \(x = \frac{{ - 5}}{6}\).

c)

\(\begin{array}{l}\frac{2}{5}:x = \frac{1}{{16}}:0,125\\\frac{2}{5}:x = \frac{1}{{16}}:\frac{1}{8}\\\frac{2}{5}:x = \frac{1}{{16}}.8\\\frac{2}{5}:x = \frac{1}{2}\\x = \frac{2}{5}:\frac{1}{2}\\x = \frac{2}{5}.2\\x = \frac{4}{5}\end{array}\)      

Vậy \(x = \frac{4}{5}\)

d)

\(\begin{array}{l} - \frac{5}{{12}}x = \frac{2}{3} - \frac{1}{2}\\ - \frac{5}{{12}}x = \frac{4}{6} - \frac{3}{6}\\ - \frac{5}{{12}}x = \frac{1}{6}\\x = \frac{1}{6}:\left( { - \frac{5}{{12}}} \right)\\x = \frac{1}{6}.\frac{{ - 12}}{5}\\x = \frac{{ - 2}}{5}\end{array}\)

Vậy \(x = \frac{{ - 2}}{5}\).

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