27 + 5 = 32
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a) Ta có \(0,625^{200}=\left(\dfrac{5}{8}\right)^{200}\) và \(0,5^{1000}=\left(\dfrac{1}{2}\right)^{1000}=\left(\dfrac{1}{2}\right)^{5.200}\) \(=\left[\left(\dfrac{1}{2}\right)^5\right]^{200}\) \(=\left(\dfrac{1}{32}\right)^{200}\). Mà hiển nhiên \(\left(\dfrac{5}{8}\right)^{200}>\left(\dfrac{1}{32}\right)^{200}\) nên suy ra \(0,625^{200}>0,5^{1000}\)
b) Ta thấy \(\left(-32\right)^{27}< 0\) trong khi \(\left(-27\right)^{32}>0\) nên đương nhiên \(\left(-32\right)^{27}< \left(-27\right)^{32}\)
c) Ta thấy \(-\dfrac{3}{2}>-2\) nên \(\left(-\dfrac{3}{2}\right)^5>\left(-2\right)^5\)

2/3 x 4/5 + 4/5 x 8/3 = 4/5 x (2/3 + 8/3) = 4/5 x 10/3 = 8/3
27/32 x 16/9 -27/32 x7/9 + 27/32
= 27/32 x (16/9 - 7/9 + 1 )
=27/32 x 2
=27/16
\(\frac{2}{3}\) x \(\frac{4}{5}\) + \(\frac{4}{5}\) x \(\frac{8}{3}\)
=\(\frac{4}{5}\) x ( \(\frac{2}{3}\) + \(\frac{8}{3}\) )
= \(\frac{4}{5}\) x \(\frac{10}{3}\)
= \(\frac{40}{15}\) = \(\frac{8}{5}\)

a) `27 .75 + 25.27 -150`
`=27 xx (75 + 25)-150`
`=27 xx 100-150`
`=2700-150`
`=2550`
b) `142-[50-(2^3 .10-2^3 .5)]`
`=142-[50-2^3 .(10-5)]`
`=142-(50-8 .5)`
`=142-(50-40)`
`=142-10`
`=132`
c) `375:{32-[4+(5.3^2-42)]}-14`
`=375:{32-[4+(45-42)]}-14`
`=375:[32-(4+3)]-14`
`=375: 25 -14`
`=15-14`
`=1`
a. 27 . 75 + 25 . 27 - 150
= 27. (75 + 25) - 150
= 27 . 100 - 150
= 2700 - 150
= 2550
b. 142 - [50 - (23.10 - 23.5)]
= 142 - [50 - (8 . 10 - 8 . 5)]
= 142 - {50 - [8 . (10 - 5)]}
= 142 - (50 - 40)
= 142 - 10
= 132
c. 375 : {32 – [ 4 + (5. 32 – 42)]} – 14
= 375 : {32 – [ 4 + (5. 9 – 42)]} – 14
= 375 : {32 – [ 4 + (45 – 42)]} – 14
= 375 : {32 – [ 4 + 3]} – 14
= 375 : {32 –7} – 14
= 375 : 25 - 14
= 15 - 14
= 1

\(\left(-27\right)^5:32^3\)
\(=\left[\left(-3\right)^3\right]^5:\left(2^5\right)^3\)
\(=\left(-3\right)^{15}:2^{15}\)
\(=\left(-3:2\right)^{15}\)
\(=\left(-\dfrac{3}{2}\right)^{15}\)
\(\left(-27\right)^5\):\(32^3\)
=-14348907:32768
=-437,8938904
tìm x
a/\(\dfrac{x}{2}=\dfrac{32}{x}\)
b/\(\dfrac{5}{25}=5\)
c/\(\dfrac{30^x}{27^x}=27\)
d/5x . 10x=2500


\(=\left(\dfrac{-12+5}{32}\right):\dfrac{-4}{5}+\dfrac{27}{125}+\dfrac{-5}{8}+\dfrac{27}{32}\cdot\dfrac{5}{4}\)
\(=\dfrac{-7}{32}\cdot\dfrac{-5}{4}+\dfrac{27}{125}+\dfrac{-5}{8}+\dfrac{135}{128}\)
\(=\dfrac{100}{128}+\dfrac{27}{125}-\dfrac{5}{8}\)
\(=\dfrac{1489}{4000}\)

32/5 : 32/25 - 27/37 * 32/3
32/5 * 25/32 - 27/37 * 32/3
5 - 288/37
-103/37
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