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Ta có:
(-1/5)300 = (-1)300/5300 = 1/(53)100 = 1/125100
(-1/3)500 = (-1)500/3500 = 1/(35)100 = 1/243100
Vì 125100 < 243100
=> 1/125100 > 1/243100
=> (-1/5)300 > (-1/3)500
Ta có : \(\left(-\frac{1}{5}\right)^{300}=\left(-\frac{1}{5}\right)^{3.100}=\left(-\frac{1}{125}\right)^{100}=\left(\frac{1}{125}\right)^{100}\)
\(\left(-\frac{1}{3}\right)^{500}=\left(-\frac{1}{3}\right)^{5.100}=\left(-\frac{1}{243}\right)^{100}=\left(\frac{1}{243}\right)^{100}\)
Mà \(125< 243\Rightarrow\frac{1}{125}>\frac{1}{243}\Rightarrow\left(\frac{1}{125}\right)^{100}>\left(\frac{1}{243}\right)^{100}\)
\(=>\left(-\frac{1}{5}\right)^{300}>\left(-\frac{1}{3}\right)^{500}\)
\(\left(\frac{1}{3}\right)^{500}=\left(\frac{1}{3}^5\right)^{100}=\frac{1}{243}^{100}\)
\(\left(\frac{1}{5}\right)^{300}=\left(\frac{1}{5}^3\right)^{100}=\frac{1}{125}^{100}\)
Vì \(\frac{1}{243}<\frac{1}{125}=>\frac{1}{243}^{100}<\frac{1}{125}^{100}=>\left(\frac{1}{3}\right)^{500}<\left(\frac{1}{5}\right)^{300}\)
3-500=(35)-100= 243-100
5-300= (53)-100 =125-100
243>125 => 243-100<125-100
Hay 3-500 <5-300
a) Ta có :\(\left(\frac{-1}{5}\right)^{300}=\frac{-1^{300}}{5^{300}}=\frac{1}{125^{100}}\)
\(\left(\frac{-1}{3}\right)^{500}=\frac{-1^{500}}{3^{500}}=\frac{1}{243^{100}}\)
Mà \(\frac{1}{125^{100}}>\frac{1}{243^{100}}\)
\(\Rightarrow\left(\frac{-1}{5}\right)^{300}>\left(\frac{-1}{3}\right)^{500}\)
b)Ta có :\(2^{90}=\left(2^{15}\right)^6=32768^6\)
\(5^{36}=\left(5^6\right)^6=15625^6\)
Vì \(32768^6>15625^6\Rightarrow2^{90}>5^{36}\)
a.Ta có: \(\left(\frac{-1}{5}\right)^{300}=\left(\frac{-1}{5}^3\right)^{100}=\left(\frac{-1}{125}\right)^{100}=\left(\frac{1}{125}\right)^{100}\)
\(\left(\frac{-1}{3}\right)^{500}=\left(\frac{-1}{3}^5\right)^{100}=\left(\frac{-1}{243}\right)^{100}=\left(\frac{1}{234}\right)^{100}\)
Mà: \(\frac{1}{125}>\frac{1}{234}\Rightarrow\left(\frac{1}{125}\right)^{100}>\left(\frac{1}{234}\right)^{100}\)
Vậy \(\left(\frac{-1}{5}\right)^{300}>\left(\frac{-1}{3}\right)^{500}\)
b.Ta có: \(2^{90}=\left(2^{10}\right)^9=1024^9\)
\(5^{36}=\left(5^4\right)^9=625^9\)
Mặt khác: \(1024>625\Rightarrow1024^9>625^9\)
Vậy \(2^{90}>5^{36}\)
a) \(\frac{3}{4} + \left( {\frac{1}{2} - \frac{1}{3}} \right) = \frac{9}{{12}} + \left( {\frac{6}{{12}} - \frac{4}{{12}}} \right) = \frac{9}{{12}} + \frac{2}{{12}} = \frac{{11}}{{12}}\)
\(\frac{3}{4} + \frac{1}{2} - \frac{1}{3} = \frac{9}{{12}} + \frac{6}{{12}} - \frac{4}{{12}} = \frac{{15}}{{12}} - \frac{4}{{12}} = \frac{{11}}{{12}}\)
Vậy \(\frac{3}{4} + \left( {\frac{1}{2} - \frac{1}{3}} \right)\) = \(\frac{3}{4} + \frac{1}{2} - \frac{1}{3}\)
b)\(\frac{2}{3} - \left( {\frac{1}{2} + \frac{1}{3}} \right) = \frac{4}{6} - \left( {\frac{3}{6} + \frac{2}{6}} \right) = \frac{4}{6} - \frac{5}{6} = \frac{{ - 1}}{6}\)
\(\frac{2}{3} - \frac{1}{2} - \frac{1}{3} = \frac{4}{6} - \frac{3}{6} - \frac{2}{6} = \frac{1}{6} - \frac{2}{6} = \frac{{ - 1}}{6}\)
Vậy \(\frac{2}{3} - \left( {\frac{1}{2} + \frac{1}{3}} \right)\)=\(\frac{2}{3} - \frac{1}{2} - \frac{1}{3}\).
`#3107`
`a)`
`3/4 + (1/2 - 1/3)`
`= 3/4 + (3/6 - 2/6)`
`= 3/4 + 1/6`
`= 11/12`
`3/4 + 1/2 - 1/3`
`= 9/12 + 6/12 - 4/12`
`= (9 + 6 - 4)/12`
`= 11/12`
Vì `11/12 = 11/12`
`=> 3/4 + (1/2 - 1/3) = 3/4 + 1/2 - 1/3`
`b)`
`2/3 - (1/2 + 1/3)`
`= 2/3 - (3/6 + 2/6)`
`= 2/3 - 5/6`
`= -1/6`
`2/3 - 1/2 - 1/3`
`= 4/6 - 3/6 - 2/6`
`= (4 - 3 - 2)/6`
`= -1/6`
Vì `-1/6 = -1/6`
`=> 2/3 - (1/2 + 1/3) = 2/3 - 1/2 - 1/3`
1 :\(\frac{7}{20}\)
2 \(\frac{1}{4}\)
3 \(\frac{23}{2}\)
4 2187
5 64
6 x=16
7 x=\(\frac{-1}{243}\)
8 mϵ∅
cho mình hỏi cài này là j vậy
Đề 2
1) \(\frac{7}{20}.\)
2) \(\frac{1}{4}.\)
3) \(\frac{23}{2}.\)
4) \(2187.\)
5) \(64.\)
6) \(x=16.\)
7) \(x=\left(-\frac{1}{3}\right)^5\)
8) \(m\in\varnothing.\)
Chúc bạn học tốt!
\(A=x+\left(x+\frac{1}{5}\right)+\left(x+\frac{2}{5}\right)+\left(x+\frac{3}{5}\right)+\left(x+\frac{4}{5}\right)\)
\(=5x+\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}\)
\(=5x+2\)
\(B=5x\)
\(\Rightarrow A>B\)Với \(\forall\)\(x\)
#)Giải :
\(A=\left[x\right]+\left[1+\frac{1}{5}\right]+\left[x+\frac{2}{5}\right]+\left[x+\frac{3}{5}\right]+\left[x+\frac{4}{5}\right]\)
Thay x = 3,7 vào biểu thức, ta có :
\(A=\left[3,7\right]+\left[3,7+\frac{1}{5}\right]+\left[3,7+\frac{2}{5}\right]+\left[3,7+\frac{3}{5}\right]+\left[3,7+\frac{4}{5}\right]\)
\(A=\left[3,7+3,7+3,7+3,7+3,7\right]+\left[1+\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}\right]\)
\(A=18,5+3\)
\(A=21,5\)
\(B=\left[5x\right]=\left[5\times3,7\right]=18,5\)
Vì 21,5 > 18,5 \(\Rightarrow A>B\)
x<y nhé bạn :)