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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: \(=2^2\cdot9\cdot\dfrac{1}{6\cdot9}\cdot\dfrac{4^2}{9^2}=\dfrac{2^2}{6}\cdot\dfrac{2^4}{3^4}=\dfrac{2^6}{2\cdot3\cdot3^4}=\dfrac{2^5}{3^5}=\left(\dfrac{2}{3}\right)^5\)
b: \(=2^8\cdot\dfrac{3^4}{2^4}=3^4\cdot2^4=6^4\)
c: \(=\dfrac{\left(\dfrac{1}{2}\right)^3\cdot2^3\cdot\left(\dfrac{1}{2}\right)^2}{\left(-8\right)^2\cdot16}\cdot2^6=\dfrac{\dfrac{1}{2^2}}{64\cdot16}\cdot64=\dfrac{1}{4}:16=\dfrac{1}{64}=\left(\dfrac{1}{8}\right)^2\)
a: \(=2^2\cdot9\cdot\dfrac{1}{3^3\cdot2}\cdot\dfrac{2^4}{3^4}=\dfrac{2^4\cdot2^2}{2}\cdot\dfrac{9}{3^3\cdot3^4}=\dfrac{2^5}{3^5}=\left(\dfrac{2}{3}\right)^5\)
b: \(=2^8\cdot\dfrac{3^4}{2^4}=3^4\cdot2^4=6^4\)
c: \(=\dfrac{\dfrac{1}{2^3}\cdot\dfrac{1}{2^2}\cdot8}{\left(-8\right)^2\cdot2^4}\cdot2^6=\dfrac{1}{2^2}\cdot2^6:2^{10}=\dfrac{2^4}{2^{10}}=\dfrac{1}{2^6}=\left(\dfrac{1}{8}\right)^2\)
a) \(\left(-2\right)^{240}\) và \(\left(-3\right)^{160}\)
Ta có: \(\left(-2\right)^{240}=[\left(-2\right)^3]^{80}=\left(-8\right)^{80}\)
\(\left(-3\right)^{160}=\left[\left(-3\right)^2\right]^{80}=9^{80}\)
Mà: \(\left(-8\right)^{80}< 9^{80}\) (vì -8 < 9)
Nên: \(\left(-2\right)^{240}< \left(-3\right)^{160}\)
a) \(\left(-2\right)^{210}và\left(-3\right)^{160}\)
Ta có:\(\left(-2\right)^{240}\) \(=\) \(\left[\left(-2\right)^3\right]^{80}\) \(=\) \(\left(-8\right)^{80}\)
\(\left(-3\right)^{160}\) \(=\) \(\left[\left(-3\right)^2\right]^{80}\) \(=\) \(9^{80}\)
Mà:\(\left(-8\right)^{80}\) \(< \) \(9^{80}\) (vì -8 < 9)
Nên:\(\left(-2\right)^{240}\) < \(\left(-3\right)^{160}\)
a: \(=\dfrac{3^3\cdot2^6}{3^{-4}\cdot2^6}=3^7\)
b: \(=\left(\dfrac{3}{7}\right)^5\cdot\left(\dfrac{3}{7}\right)\cdot\dfrac{5^6}{3^6}:\left(\dfrac{625}{343}\right)^2\)
\(=\dfrac{3^6}{7^6}\cdot\dfrac{5^6}{3^6}:\dfrac{5^8}{7^6}\)
\(=\dfrac{1}{5^2}\)
c: \(=5^{4+3}\cdot\left(\dfrac{5}{2}\right)^{-5}\cdot\dfrac{1}{25}\)
\(=5^5\cdot\left(\dfrac{2}{5}\right)^5=2^5\)
Nhận xét:
Lũy thừa với số mũ chẵn của một số âm là một số dương
Lũy thừa với số mũ lẻ của một số âm là một số âm
a: \(=\dfrac{3^3\cdot2^6}{3^{-4}\cdot2^6}=3^7\)
b: \(=\left(\dfrac{3}{7}\cdot\dfrac{5}{3}\right)^6\cdot\dfrac{5}{3}\cdot\dfrac{3}{7}:\left(\dfrac{7^3}{5^4}\right)^{-2}\)
\(=\left(\dfrac{5}{7}\right)^6\cdot\dfrac{5}{7}\cdot\left(\dfrac{5}{7}\right)^6\cdot5^2\)
\(=\left(\dfrac{5}{7}\right)^{13}\cdot5^2\)
c: \(=5^4\cdot2.5^{-5}\cdot125\cdot0.04\)
\(=5^4\cdot5\cdot\left(\dfrac{5}{2}\right)^{-5}\)
\(=5^5\cdot\left(\dfrac{2}{5}\right)^5=2^5\)
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
\(\left(\dfrac{1}{2}\right)^{300}=\dfrac{1}{2^{300}}=\dfrac{1}{\left(2^3\right)^{100}}=\dfrac{1}{8^{100}}\)
\(\left(\dfrac{1}{3}\right)^{200}=\dfrac{1}{3^{200}}=\dfrac{1}{\left(3^2\right)^{100}}=\dfrac{1}{9^{100}}\\ \)
\(\dfrac{1}{8^{100}}>\dfrac{1}{9^{100}}\\ \Rightarrow\left(\dfrac{1}{2}\right)^{300}>\left(\dfrac{1}{3}\right)^{200}\)
Bạn ơi so sánh \(\left(\dfrac{1}{2}\right)^{300}và\left(\dfrac{1}{3}\right)^{202}\) mà đâu phải so sánh \(\left(\dfrac{1}{2}\right)^{300}và\left(\dfrac{1}{3}\right)^{200}\)