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KV
12 tháng 9 2023
8⁵ = (2³)⁵ = 2¹⁵ = 2.2¹⁴
3.4⁷ = 3.(2²)⁷ = 3.2¹⁴
Do 2 < 3 nên 2.2¹⁴ < 3.2¹⁴
Vậy 8⁵ < 3.4⁷
12 tháng 9 2023
\(8^5=2^{15}=2.2^{14}\)
\(3.4^7=3.2^{14}>2.2^{14}\)
\(\Rightarrow8^5< 3.4^7\)
15 tháng 8 2015
\(A=\frac{3}{8^3}+\frac{7}{8^4}=\frac{3}{8^3}+\frac{3}{8^4}+\frac{4}{8^4}\)
\(B=\frac{7}{8^3}+\frac{3}{8^4}=\frac{3}{8^3}+\frac{3}{8^4}+\frac{4}{8^4}\)
\(A=\frac{3}{8^3}+\frac{3}{8^4}+\frac{4}{8^3}>B=\frac{3}{8^3}+\frac{3}{8^4}+\frac{4}{8^4}\)
vậy A>B
HM
5
26 tháng 6 2023
`@` `\text {Ans}`
`\downarrow`
`1,`
`a)`
`3^12` và `5^8`
\(3^{12}=\left(3^3\right)^4=9^4\)
\(5^8=\left(5^2\right)^4=25^4\)
Vì `9 < 25` `=> 25^4 > 9^4`
`=> 3^12 > 5^8`
Vậy, `3^12 > 5^8`
`b)`
`(0,6)^9` và `(-0,9)^6`
\(\left(0,6\right)^9=\left(0,6^3\right)^3=\left(0,216\right)^3\)
\(\left(-0,9\right)^6=\left[\left(-0,9\right)^2\right]^3=\left(0,81\right)^3\)
Vì `0,81 > 0,216 => (0,81)^3 > (0,216)^3`
`=> (0,6)^9 < (-0,9)^6`
Vậy, `(0,6)^9<(-0,9)^6`
XO
26 tháng 6 2023
1.a) Có 312 = 33.4 = 274 ;
58 = 52.4 = 254
Dễ thấy 274 > 254 nên 312 > 58
b) Có \(0,6^9=\dfrac{6^9}{10^9}=\dfrac{6^{3.3}}{10^9}=\dfrac{216^3}{10^9}\)
mà \(\left(-0,9\right)^6=0,9^6=\dfrac{9^6}{10^6}=\dfrac{9^6.10^3}{10^9}=\dfrac{9^{2.3}.10^3}{10^9}=\dfrac{81^3.10^3}{10^9}=\dfrac{810^3}{10^9}\)
Dễ thấy \(\dfrac{216^3}{10^9}< \dfrac{810^3}{10^9}\Rightarrow0,6^9< \left(-0,9\right)^6\)
CB
0
KY
2
14 tháng 6 2018
a) \(\frac{-7}{9}và\frac{3}{-8}\)
Ta có: \(\frac{-7}{9}=\frac{-56}{72}\)
\(\frac{3}{-8}=\frac{-3}{8}=\frac{-21}{72}\)
\(Vì\frac{-56}{72}< \frac{-21}{72}nên\frac{-7}{9}< \frac{3}{-8}\)
b)\(\frac{209}{310}và\frac{-718}{599}\)
Ta có: \(\frac{209}{310}>0\)
\(\frac{-718}{599}< 0\)
\(Vì\frac{209}{310}>0và\frac{-718}{599}< 0nên\frac{209}{310}>\frac{-718}{599}\)
NN
0
L
2
19 tháng 12 2021
^$@*&^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%$%%$%$%$%$%%%%%%%%%%%%%%%%%%454%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%$%$%%$$%$%$%$%$%$%$%$%$