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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)\(2^{27}=8^9;3^{18}=9^9\)
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 \(2^{27}< 3^{18}\)
b) Ta có: 227 = (23)9 = 89
...............318 = (32)9 = 99
Vì: 8 < 9
Nên: 89 < 99
Hay: 227 < 318
Bài 3:
a) \(\left(x-\frac{1}{2}\right)^2=0\)
\(\Rightarrow x-\frac{1}{2}=0\)
\(\Rightarrow x=\frac{1}{2}\)
Vậy \(x=\frac{1}{2}\)
b) \(\left(x-2\right)^2=1\)
\(\Rightarrow x-2=\pm1\)
+) \(x-2=1\Rightarrow x=3\)
+) \(x-2=-1\Rightarrow x=1\)
Vậy \(x=3\) hoặc \(x=1\)
c) \(\left(2x-1\right)^3=-8\)
\(\Rightarrow\left(2x-1\right)^3=\left(-2\right)^3\)
\(\Rightarrow2x-1=-2\)
\(\Rightarrow2x=-1\)
\(\Rightarrow x=\frac{-1}{2}\)
Vạy \(x=\frac{-1}{2}\)
d) \(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\)
\(\Rightarrow\left(x+\frac{1}{2}\right)^2=\left(\frac{1}{4}\right)^2\)
\(\Rightarrow x+\frac{1}{2}=\frac{1}{4}\)
\(\Rightarrow x=\frac{-1}{4}\)
Vậy \(x=\frac{-1}{4}\)
Ta có :
\(0,25^8==\left(0,5^2\right)^8=0,5^{16}\)
\(0,125^4=\left(0,5^3\right)^4=0,5^{12}\)
4950=(72)50=7100
2300=23.100=23.2100=8.2100
3200=32.100=32.3100=9.3100
Vì 8 < 9 và 2100 < 3100 => 2300<3200