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18 tháng 9 2017
2441=(27)63=12863
5189=(53)63=12563
Vì 128 > 125 => 12863 > 12563 => 2441 > 5189
NN
2
13 tháng 12 2019
Xét: \(\frac{\left(17^{2017}+16^{2017}\right)^{2018}}{17^{2017.2018}}=\left(\frac{17^{2017}+16^{2017}}{17^{2017}}\right)^{2018}=\left(1+\left(\frac{16}{17}\right)^{2017}\right)^{2018}\)
\(\frac{\left(17^{2018}+16^{2018}\right)^{2017}}{17^{2017.2018}}=\left(\frac{17^{2018}+16^{2018}}{17^{2018}}\right)^{2017}=\left(1+\left(\frac{16}{17}\right)^{2018}\right)^{2017}\)
Ta có: \(0< \frac{16}{17}< 1\)
=> \(\left(\frac{16}{17}\right)^{2017}>\left(\frac{16}{17}\right)^{2018}\)
=> \(1+\left(\frac{16}{17}\right)^{2017}>1+\left(\frac{16}{17}\right)^{2018}>1\)
=> \(\left(1+\left(\frac{16}{17}\right)^{2017}\right)^{2018}>\left(1+\left(\frac{16}{17}\right)^{2018}\right)^{2017}\)
=> \(\left(17^{2017}+16^{2017}\right)^{2018}>\left(17^{2018}+16^{2018}\right)^{2017}\)
CD
1
T
14 tháng 9 2019
Có:
\(2^{20}=\left(2^5\right)^4=32^4\)
\(5^{12}=\left(5^3\right)^4=125^4\)
Do 125 > 32 nên \(125^4>32^4\Leftrightarrow2^{20}>5^{12}\)
Vậy..
cảm ơn nhìu
19 tháng 9 2016
1)Ta có \(\left(\frac{1}{16}\right)^{10}\)=\(\left[\left(\frac{1}{2}\right)^4\right]^{10}\)=\(\left(\frac{1}{2}\right)^{40}\)
Vì \(2^{40}\)<\(2^{50}\)=>\(\left(\frac{1}{2}\right)^{40}\)>\(\left(\frac{1}{2}\right)^{50}\)
19 tháng 9 2016
1) \(\left(\frac{1}{16}\right)^{10}=\left(\frac{1^4}{2^4}\right)^{10}=\left[\left(\frac{1}{2}\right)^4\right]^{10}=\left(\frac{1}{2}\right)^{40}\)
Vì \(\left(\frac{1}{2}\right)^{40}< \left(\frac{1}{2}\right)^{50}\) nên \(\left(\frac{1}{16}\right)^{10}< \left(\frac{1}{2}\right)^{50}\)
2) \(64^8=\left(4^3\right)^8=4^{24}\)
\(16^{12}=\left(4^2\right)^{12}=4^{24}\)
Vì \(4^{24}=4^{24}\) nên \(64^8=16^{12}\)
19 tháng 7 2019
bài 2
làm câu B;C nha
B)
\(27^3=\left(3^3\right)^3=3^9\)
\(9^5=\left(3^2\right)^5=3^{10}\)
vì \(10>9\)
\(=>9^5>27^3\)
C)
\(\left(\frac{1}{8}\right)^6=\left(\frac{1}{2^3}\right)^6=\frac{1^6}{2^{18}}=\frac{1}{2^{18}}\)
\(\left(\frac{1}{32}\right)^4=\left(\frac{1}{2^5}\right)^4=\frac{1^4}{2^{20}}=\frac{1}{2^{20}}\)
vì \(2^{18}< 2^{20}\)
\(=>\frac{1}{2^{18}}>\frac{1}{2^{20}}\)
\(=>\left(\frac{1}{8}\right)^6>\left(\frac{1}{32}\right)^4\)
19 tháng 7 2019
\(\text{A.}\frac{32^3.9^5}{8^3.6^6}=\frac{\left(2^5\right)^3.\left(3^2\right)^5}{\left(2^3\right)^3.\left(2.3\right)^6}=\frac{2^{15}.3^{10}}{2^9.2^6.3^6}=\frac{3^{10}}{3^6}=3^4=81\)
\(\text{B.}\frac{\left(5^5-5^4\right)^3}{50^6}=\frac{2500^3}{50^6}=\frac{\left(50^2\right)^3}{50^6}=\frac{50^6}{50^6}=1\)
Bài 2:
\(\text{A.Ta có:}\)
\(5^6=\left(5^3\right)^2=125^2\)
\(\left(-2\right)^{14}=2^{14}=\left(2^7\right)^2=128^2\)
Vì \(125< 128\)
\(\Rightarrow125^2< 128^2\)
\(\Rightarrow5^6< \left(-2\right)^{14}\)
\(\text{B.Ta có:}\)
\(9^5=\left(3^2\right)^5=3^{10}\)
\(27^3=\left(3^3\right)^3=3^9\)
Vì \(9< 10\)
\(\Rightarrow3^9< 3^{10}\)
\(\Rightarrow27^3< 9^5\)
\(\text{C.Ta có:}\)
\(\left(\frac{1}{8}\right)^6=\left[\left(\frac{1}{2}\right)^3\right]^6=\left(\frac{1}{2}\right)^{18}\)
\(\left(\frac{1}{32}\right)^4=\left[\left(\frac{1}{2}\right)^5\right]^4=\left(\frac{1}{2}\right)^{20}\)
Vì \(18< 20\)
\(\Rightarrow\left(\frac{1}{2}\right)^{18}< \left(\frac{1}{2}\right)^{20}\)
\(\Rightarrow\left(\frac{1}{8}\right)^6< \left(\frac{1}{32}\right)^4\)
1 tháng 11 2020
\(\text{Theo đề ta có :}\)
\(\frac{\left(-1\right)^6\cdot3^5\cdot4^3}{9^2\cdot2^5}\)
= \(\frac{1\cdot3^5\cdot\left(2^2\right)^3}{\left(3^2\right)^2\cdot2^5}\) = \(\frac{3^5\cdot2^6}{3^4\cdot2^5}=\frac{3^4\cdot3\cdot2^5\cdot2}{3^4\cdot2^5}=3\cdot2=6\)
S
4 tháng 9 2019
\(5^a+25\)
\(+,a=0\Rightarrow5^a+25=26\left(l\right)\)
\(+,a=1\Rightarrow5^a+25=30\left(l\right)\)
\(+,a=2\Rightarrow5^a+25=50\left(l\right)\)
\(+,a=3\Rightarrow5^a+25=150\left(l\right)\)
\(+,a\ge4\Rightarrow5^a=\left(....25\right)+25=\left(....50\right)\Rightarrow\hept{\begin{cases}5^a+25⋮2\\5^a+25⋮4̸\end{cases}}\left(l\right)\)
Ta có: 2441 = (27)63 = 12863
5189 = (53)63 = 12563
Vì 128 > 125
=> 12863 > 12563
=> 2441 > 5189