Bài 1:
a, `(2/3)^3 - 4 · (-1 3/4)^2 + (-2/3)^3`
`= 2^3/3^3 - 4 · (frac{-7}{4})^2 + (-2)^3/3^3`
`= 8/27 - 4 · (-7)^2/4^2 + frac{-8}{27}`
`= -4 · frac{-49}{16}`
`= 49/4`
b, `(-0,5)^5 : (-0,5)^3 - (17/2)^7 : (17/2)^6`
`= (-0,5)^2 - 17/2`
`= 1/4 - 17/2`
`= 1/4 - 34/4`
`= frac{-33}{4}`
Bài 2:
a, `frac{3^17 · 81^11}{27^10 · 9^15}`
`= frac{3^17 · (3^4)^11}{(3^3)^10 · (3^2)^15}`
`= frac{3^17 · 3^44}{3^30 · 3^30}`
`= frac{3^61}{3^60}`
`= 3`
b, `frac{9^2 · 2^11}{16^2 · 6^3}`
`= frac{9^2 · 2^11}{(2^4)^2 · 6^3}`
`= frac{9^2 · 2^11}{2^8 · 6^3}`
`= frac{9^2 · 2^3}{6^3}`
`= frac{81 · 8}{216}`
`= frac{648}{216} = 3`
Bài 3:
a, `2x + 1^2 = 36`
`2x + 1 = 36`
`2x = 35`
`x = 35/2`
Vậy `x = 35/2`
b, `2x -1^3 = -8`
`2x - 1 = -8`
`2x = -7`
`x = frac{-7}{2}`
Vậy `x = frac{-7}{2}`
c, `2^{3x} = 1/8`
`8^x = 1/8`
`x = 1/8 : 8`
`x = 1/8 · 1/8`
`x = 1/64`
Vậy `x = 1/64`
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