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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 \(2^{90}>5^{36}\)
Bài 1: \(\left(\frac{-1}{16}\right)^{100}=\frac{1}{\left(2^4\right)^{100}}=\frac{1}{2^{400}}>\frac{1}{2^{500}}=\left(\frac{-1}{2}\right)^{500}.\)
Bài 2: \(100^{99}+1>100^{68}+1\Rightarrow\frac{1}{100^{99}+1}< \frac{1}{100^{68}+1}\Rightarrow\frac{-99}{100^{99}+1}>\frac{-99}{100^{68}+1}\)
\(\Rightarrow100+\frac{-99}{100^{99}+1}>100+\frac{-99}{100^{68}+1}\Rightarrow\frac{100^{100}+1}{100^{99}+1}>\frac{100^{69}+1}{100^{68}+1}\)
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!
x<y nhé bạn :)