bài 4: so sánh
a) \(\left(\frac{-1}{5}\right)^{300}\) và \(\left(\frac{-1}{3}\right)^{500}\)
b) \(-\left(-2\right)^{300}\) và \(\left(-3\right)^{200}\)
giúp mk với mai mk nộp rồi thanks nhiều 
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NT
21 tháng 10 2017
a) \(=\left(\frac{-1}{5}^3\right)^{100}va\left(\frac{-1}{3}^5\right)^{100}\)
\(=\left(\frac{-1}{125}\right)^{100}va\left(\frac{-1}{243}\right)^{100}\)
Mà \(\frac{-1}{125}>\frac{-1}{243}\)
\(\Rightarrow\left(\frac{-1}{5}\right)^{300}>\left(\frac{-1}{3}\right)^{500}\)
b)\(2^{27}=8^9;3^{18}=9^9\)
TM
14 tháng 9 2016
Ta có:
\(\left(\frac{1}{2}\right)^{225}=\left[\left(\frac{1}{2}\right)^9\right]^{25}=\left(\frac{1}{516}\right)^{25}\)
\(\left(\frac{1}{3}\right)^{100}=\left[\left(\frac{1}{3}\right)^4\right]^{25}=\left(\frac{1}{81}\right)^{25}\)
\(\frac{1}{516}< \frac{1}{81}\Rightarrow\left(\frac{1}{516}\right)^{25}< \left(\frac{1}{81}\right)^{25}\Rightarrow\left(\frac{1}{2}\right)^{225}< \left(\frac{1}{3}\right)^{100}\)
12 tháng 10 2016
ta có:1/8^100
-1/4^200=(-1/4^2)^100=1/16^100
=>1/8^100 >1/16^100
=>1/8^100 >-1/4^200
KT
3
21 tháng 7 2016
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
HT
21 tháng 7 2016
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 \(125< 243\Rightarrow\frac{1}{125}>\frac{1}{243}\Rightarrow\left(\frac{1}{125}\right)^{100}>\left(\frac{1}{243}\right)^{100}\)
\(=>\left(-\frac{1}{5}\right)^{300}>\left(-\frac{1}{3}\right)^{500}\)
21 tháng 10 2017
a) \(\left(-\dfrac{1}{5}\right)^{300}=\left(-\dfrac{1}{5}\right)^{3.100}=\left(-\dfrac{1}{125}\right)^{100}\)
\(\left(-\dfrac{1}{3}\right)^{500}=\left(-\dfrac{1}{3}\right)^{5.100}=\left(-\dfrac{1}{243}\right)^{100}\)
Vì \(\left(-\dfrac{1}{125}\right)^{100}< \left(-\dfrac{1}{243}\right)^{100}\)
Nên \(\left(-\dfrac{1}{5}\right)^{300}< \left(-\dfrac{1}{3}\right)^{500}\)
b) \(2^{27}=2^{3.9}=\left(2^3\right)^9=8^9\)
\(3^{18}=3^{2.9}=\left(3^2\right)^9=9^9\)
Vì \(8^9< 9^9\)nên \(2^{27}< 3^{18}\)
GH
21 tháng 10 2017
b) Ta có: 227 = (23)9 = 89
...............318 = (32)9 = 99
Vì: 8 < 9
Nên: 89 < 99
Hay: 227 < 318
22 tháng 10 2016
a) \(\left|x+\frac{1}{2}\right|=\left|2x+3\right|\)
\(\Rightarrow\left[\begin{array}{nghiempt}x+\frac{1}{2}=2x+3\\x+\frac{1}{2}=-\left(2x+3\right)\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}2x-x=\frac{1}{2}-3\\x+\frac{1}{2}=-2x-3\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{-5}{2}\\x+2x=-3-\frac{1}{2}\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{-5}{2}\\3x=\frac{-7}{2}\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{-5}{2}\\x=\frac{-7}{6}\end{array}\right.\)
Vậy \(x\in\left\{\frac{-5}{2};\frac{-7}{6}\right\}\)
LY
22 tháng 10 2016
\(\left|x+\frac{1}{2}\right|=\left|2x+3\right|\)
\(Ta\) \(có\): \(x+\frac{1}{2}=2x+3\)
\(x+\frac{1}{2}=x+x+3\\\)
\(x+\frac{1}{2}=x+\left(x+3\right)\)
\(\Rightarrow\frac{1}{2}=x+3\)
\(\Rightarrow x=\frac{1}{2}-3\)
\(\Rightarrow x=-\frac{5}{2}\)
Vậy \(x=-\frac{5}{2}\)
b, \(\left|x+\frac{1}{5}\right|+\left|x+\frac{2}{5}\right|+\left|x+1\frac{2}{5}\right|=4x\)
\(Ta\) \(có\)
\(x+\frac{1}{5}+x+\frac{2}{5}+x+1\frac{2}{5}\)\(=4x\)
\(3x+\left(\frac{1}{5}+\frac{2}{5}+1\frac{2}{5}\right)=4x\)
\(3x+2=4x\)
\(3x+2=3x+x\)
\(\Rightarrow x=2\)
Vậy \(x=2\)
2 tháng 11 2017
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 \(32768^6>15625^6\Rightarrow2^{90}>5^{36}\)
HB
2 tháng 11 2017
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 \(2^{90}>5^{36}\)
Ta có : (-1/5)^300=(-1/5^3)100=(-1/125)^100
(-1/3)^500=(-1/3^5)^100=(-1/243)^100
vì (-1/243)^100<(-1/125)^100→(-1/5)^300>(-1/3)^500
b, ta có:-(-2)^300=(2^3)^100=8^100
(-3)^200=(-3^2)^100=9^100
vì 8^100<9^100→-(-2)^300<(-3)^200