So sánh \(\left(\frac{1}{80}\right)^7\) với \(\left(\frac{1}{243}\right)^6\)
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CO
3
TS
25 tháng 5 2015
\(\left(\frac{1}{80}\right)^7>\left(\frac{1}{81}\right)^7=\left(\frac{1}{3^4}\right)^7>\left(\frac{1}{3^5}\right)^6=\left(\frac{1}{243}\right)^6\)
25 tháng 5 2015
\(\left(\frac{1}{80}\right)^7>\left(\frac{1}{81}\right)^7=\left(\frac{1}{3^4}\right)^7=\frac{1^7}{\left(3^4\right)^7}=\frac{1}{3^{28}}\)
\(\left(\frac{1}{243}\right)^6=\left(\frac{1}{3^5}\right)^6=\frac{1^6}{\left(3^5\right)^6}=\frac{1}{3^{30}}\)
Vì \(\frac{1}{3^{28}}>\frac{1}{3^{30}}\) nên \(\left(\frac{1}{80}\right)^7>\left(\frac{1}{243}\right)^6\)
H
2
VM
22 tháng 2 2017
a) 80<243 nên \(\frac{1}{80}>\frac{1}{243}\)
\(\Rightarrow\left(\frac{1}{80}\right)^7>\left(\frac{1}{243}\right)^7\) mà \(\left(\frac{1}{243}\right)^7>\left(\frac{1}{243}\right)^6\)
Nên \(\left(\frac{1}{80}\right)^7>\left(\frac{1}{243}\right)^6\)
b) Ta so sánh \(\frac{3}{8}\) với \(\frac{5}{243}\)
Ta có: \(\frac{3}{8}=\frac{3.243}{8.243}=\frac{729}{1944}\)
\(\frac{5}{243}=\frac{5.8}{243.8}=\frac{40}{1944}\)
Suy ra: \(\frac{3}{8}>\frac{5}{243}\)
\(\Rightarrow\left(\frac{3}{8}\right)^5>\left(\frac{5}{243}\right)^5\) mà \(\left(\frac{5}{243}\right)^5>\left(\frac{5}{243}\right)^3\)
Nên \(\left(\frac{3}{8}\right)^5>\left(\frac{5}{243}\right)^3\)
3 tháng 3 2018
a) \(\left(\frac{1}{80}\right)^7>\left(\frac{1}{81}\right)^7=\left(\frac{1}{3^4}\right)^7=\frac{1}{3^{4.7}}=\frac{1}{3^{28}}\)
\(\left(\frac{1}{243}\right)^6=\left(\frac{1}{3^5}\right)^6=\frac{1}{3^{3.6}}=\frac{1}{3^{30}}\)
Vì \(\frac{1}{3^{28}}< \frac{1}{3^{30}}\left(3^{28}< 3^{30}\right)\)
Nên \(\left(\frac{1}{80}\right)^7< \left(\frac{1}{243}\right)^6\)
b) \(\left(\frac{3}{8}\right)^5=\frac{3^5}{\left(2^3\right)^5}=\frac{243}{2^{3.5}}=\frac{243}{2^{15}}>\frac{243}{3^{15}}>\frac{125}{3^{15}}\)
\(=\frac{5^3}{\left(3^5\right)^3}=\frac{5^3}{3^{5.3}}=\frac{5^3}{3^{15}}=\left(\frac{5}{243}\right)^3\)
\(\Rightarrow\left(\frac{3}{8}\right)^5>\left(\frac{5}{243}\right)^3\)
\(\left(\frac{1}{80}\right)^7>\left(\frac{1}{81}\right)^7=\left(\frac{1}{3^4}\right)^7=\frac{1^7}{\left(3^4\right)^7}=\frac{1}{3^{28}}\)
\(\left(\frac{1}{243}\right)^6=\left(\frac{1}{3^5}\right)^6=\frac{1^6}{\left(3^5\right)^6}=\frac{1}{3^{30}}\)
Vì \(\frac{1}{3^{28}}>\frac{1}{3^{30}}\) nên \(\left(\frac{1}{80}\right)^7>\left(\frac{1}{243}\right)^6\)