Đáp án:
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`1,`
`x ÷ (-1/3)^3 = (-1)/3`
`↔ x = (-1)/3× (-1/3)^3`
`↔ x = (-1/3)^4`
`↔ x = 1/81`
Vậy `x = 1/81`
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`2,`
`(4/5)^5 × x = (4/5)^7`
`↔ x = (4/5)^7 ÷ (4/5)^5`
`↔x = (4/5)^2`
`↔ x = 16/25`
Vậy `x = 16/25`
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`3,`
`(x + 1/2)^2 = 1/16`
`↔` \(\left[ \begin{array}{l}(x+\dfrac{1}{2})^2=(\dfrac{1}{4})^2\\(x+\dfrac{1}{2})^2=(\dfrac{-1}{4})^2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x+\dfrac{1}{2} =\dfrac{1}{4}\\x+\dfrac{1}{2}=\dfrac{-1}{4}\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=\dfrac{1}{4}-\dfrac{1}{2}\\x=\dfrac{-1}{4}-\dfrac{1}{2}\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=\dfrac{-1}{4}\\x=\dfrac{-3}{4}\end{array} \right.\)
Vậy `x=(-1)/4` hoặc `x=(-3)/4`
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`4,`
`(3x+1)^3=-27`
`↔ (3x+1)^3=(-3)^3`
`↔ 3x+1=-3`
`↔3x =-3 - 1`
`↔3x=-4`
`↔x=-4÷3`
`↔ x=(-4)/3`
Vậy `x=(-4)/3`
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`5,`
`(1/2)^2 × x = (1/2)^5`
`↔ x = (1/2)^5 ÷ (1/2)^2`
`↔ x = (1/2)^3`
`↔ x = 1/8`
Vậy `x=1/8`
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`6,`
`(-1/3)^3 × x= 1/81`
`↔ (-1/3)^3 × x = (1/3)^4`
`↔ x = (1/3)^4 ÷ (-1/3)^3`
`↔ x = (-1)/3`
Vậy `x=(-1)/3`
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`7,`
`(2x-3)^2 = 16`
`↔` \(\left[ \begin{array}{l}(2x-3)^2=4^2\\(2x-3)^2=(-4)^2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}2x-3=4\\2x-3=-4\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}2x=4+3\\2x=-4+3\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}2x=7\\2x=-1\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=7÷2\\x=-1÷2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=\dfrac{7}{2}\\x=\dfrac{-1}{2}\end{array} \right.\)
Vậy `x=7/2` hoặc `x=(-1)/2`
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`8,`
`(x-2/3)^3=1/27`
`↔ (x-2/3)^3=(1/3)^3`
`↔ x - 2/3 = 1/3`
`↔ x = 1/3 + 2/3`
`↔ x = 1`
Vậy `x=1`
