Question

Tìm x, biết rằng :

a) x : ( -\(\frac{1}{3}\) )³ = -\(\frac{1}{3}\)

b) ( \(\frac{4}{5}\) )⁵ . x = ( \(\frac{4}{5}\) )⁷

c) ( x + \(\frac{1}{2}\) )² = \(\frac{1}{16}\)

d) ( 3x + 1 )³ = -27

Các bạn giúp mình với, thanks !

Answer 1

a) x : \(\left(-\frac{1}{3}\right)^3=-\frac{1}{3}\)

\(x:\frac{-1}{27}=\frac{-1}{3}\)

\(x=\frac{-1}{3}.\frac{-1}{27}\)

\(x=\frac{1}{81}\)

Vậy \(x=\frac{1}{81}\)

Answer 2

a) \(x:\left(-\frac{1}{3}\right)^3=-\frac{1}{3}\)

\(\Leftrightarrow x=\left(-\frac{1}{3}\right)\cdot\left(-\frac{1}{3}\right)^3\)

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

\(\Leftrightarrow x=\frac{1}{81}\)

b)\(\left(\frac{4}{5}\right)^5\cdot x=\left(\frac{4}{5}\right)^7\)

\(\Leftrightarrow x=\left(\frac{4}{5}\right)^7:\left(\frac{4}{5}\right)^5=\left(\frac{4}{5}\right)^2=\frac{16}{25}\)

c)\(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\)

\(\Leftrightarrow x+\frac{1}{2}=\frac{1}{4}\)

\(\Leftrightarrow x=-\frac{1}{4}\)

d)\(\left(3x+1\right)^3=-27\)

\(\Leftrightarrow3x+1=-3\)

\(\Leftrightarrow3x=-4\)

\(\Leftrightarrow x=-\frac{4}{3}\)

Answer 3

a ) \(x:\left(-\frac{1}{3}\right)^3=-\frac{1}{3}\)

\(x=-\frac{1}{3}.\left(-\frac{1}{3}\right)^3\)

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

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

\(x=\frac{1}{81}\)

b ) \(\left(\frac{4}{5}\right)^5.x=\left(\frac{4}{5}\right)^7\)

\(x=\left(\frac{4}{5}\right)^7:\left(\frac{4}{5}\right)^5\)

\(x=\left(\frac{4}{5}\right)^{7-5}\)

\(x=\left(\frac{4}{5}\right)^2\)

\(x=\frac{16}{25}\)

c ) \(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\)

\(\left(x+\frac{1}{2}\right)=\sqrt{\frac{1}{16}}\)

\(\left(x+\frac{1}{2}\right)=\frac{1}{4}\)

\(x=-\frac{1}{4}\)

d ) \(\left(3x+1\right)^3=-27\)

\(\left(3x+1\right)=-\sqrt[3]{27}\)

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

\(3x=-2\)

\(x=-\frac{2}{3}\)

Answer 4

b) \(\left(\frac{4}{5}\right)^5.x=\left(\frac{4}{5}\right)^7\)

\(x=\left(\frac{4}{5}\right)^7:\left(\frac{4}{5}\right)^5\)

\(x=\left(\frac{4}{5}\right)^{7-5}\)

\(x=\left(\frac{4}{5}\right)^2\)

\(x=\frac{16}{25}\)

Vậy \(x=\frac{16}{25}\)

 

 

Answer 5

c) \(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\)

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

\(\Rightarrow x+\frac{1}{2}=\frac{1}{4}\)

\(x=\frac{1}{4}-\frac{1}{2}\)

\(x=-\frac{1}{4}\)

Vậy \(x=-\frac{1}{4}\)

Answer 6

d) \(\left(3x+1\right)^3=-27\)

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

\(\Rightarrow3x+1=-3\)

\(3x=-3-1\)

\(3x=-4\)

\(x=-4:3\)

\(x=\frac{-4}{3}\)

Vậy \(x=-\frac{4}{3}\)