So sánh
\(\left(17^5\right)^2va17^{10}\)
\(2^{60}va4^{20}\)
\(5^{45}va25^{15}\)
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+) Ta có: (175)2 = 175.2 = 1710
Ta thấy: 1710 = 1710 => (175)2 = 1710
+) Ta có: 420 = (22)20 = 22.20 = 240
Ta thấy: 260 > 240 => 260 > 420
+) Ta có: 2515 = (52)15 = 52.15 = 530
Ta thấy: 545 > 530 => 545 > 2515
+) Ta có: 648 = (43)8 = 43.8 = 424
1612 = (42)12 = 42.12 = 424
Ta thấy: 424 = 424 => 648 = 1612
60^5 và 15^10 ta có: 15^10= (15^2)^5= 225^5
=> 60^5 >15^10
1/20^7 và 1/5^9 ta có 20^7>5^9
=> 1/20^7 <1/5^9
Bài 1:
Ta có:
\(\left(\frac{1}{10}\right)^{15}=\left(\frac{1}{5}\right)^{3.5}=\left(\frac{1}{125}\right)^5\)
\(\left(\frac{3}{10}\right)^{20}=\left(\frac{3}{10}\right)^{4.5}=\left(\frac{81}{10000}\right)^5\)
Lại có:
\(\frac{1}{125}=\frac{80}{10000}< \frac{81}{10000}\Rightarrow\left(\frac{1}{125}\right)^5< \left(\frac{81}{10000}\right)^5\)
\(\Rightarrow\left(\frac{1}{10}\right)^{15}< \left(\frac{3}{10}\right)^{20}\)
Bài 2:
Ta có:
\(A=\frac{13^{15}+1}{13^{16}+1}\Rightarrow13A=\frac{13^{16}+13}{13^{16}+1}=1+\frac{12}{13^{16}+1}\)
\(B=\frac{13^{16}+1}{13^{17}+1}\Rightarrow13B=\frac{13^{17}+13}{13^{17}+1}=1+\frac{12}{13^{17}+1}\)
Mà \(\frac{12}{13^{16}+1}>\frac{12}{13^{17}+1}\)
\(\Rightarrow1+\frac{12}{13^{16}+1}>1+\frac{12}{13^{17}+1}\)
\(\Rightarrow13A>13B\Rightarrow A>B\)
=\(\left[\dfrac{\left(0,4.2\right)^5}{\left(0,4\right)^6}+\dfrac{2^9.2^6.3^8}{\left(3.2\right)^6.2^9}\right]=\left[\dfrac{\left(0,4\right)^5.2^5}{\left(0,4\right)^6}+\dfrac{2^6.3^8}{3^6.2^6}\right]\)
=\(\left[\dfrac{2^5}{0,4}+3^2\right]\)
=\(\left[80+9\right]=89\)
\(\left[\dfrac{\left(2.0,4\right)^5}{0,4,0,4^5}+\dfrac{2^{15}.3^8}{3^6.2^6.2^9}\right]\div\dfrac{3^{20}.5^{30}}{3^{15}.5^{30}}\)
\(=\left[\dfrac{2^5.0.4^5}{0,4.0,4^5}+\dfrac{2^{15}.3^8}{3^6.2^{15}}\right]\div3^5\)
\(=\left[\dfrac{2^5}{0,4}+3^2\right]\div243\)
\(=80+\left(3^5\div3^2\right)\)
\(=80+3^3\)
\(=80+27\)
\(=107\)
\(a=\left(15^2\right)^{60}:25^{60}\)
\(a=225^{60}:25^{60}\)
\(a=\left(225:25\right)^{60}=9^{60}\)
\(b=2^{45}.2^{15}.2^{120}\)
\(b=2^{180}=8^{60}\)
vì \(8^{60}< 9^{60}\)nên b<a
1,\(\left(\frac{4}{5}\right)^{2x+7}=\left(\frac{4}{5}\right)^{-4}\)
\(\Rightarrow\)2x+7=-4
2x=-11
x=-5,5
Ta có:
\(\left(\dfrac{1}{10}\right)^{15}=\left(\left(\dfrac{1}{10}\right)^3\right)^5=\left(\dfrac{1}{1000}\right)^5\)
\(\left(\dfrac{3}{10}\right)^{20}=\left(\left(\dfrac{3}{10}\right)^4\right)^5=\left(\dfrac{81}{10000}\right)^5\)
Ta có: \(\left(\dfrac{1}{10}\right)^{15}=\left(\dfrac{1}{10}^3\right)^5=\left(\dfrac{1}{1000}\right)^5\)
\(\left(\dfrac{3}{10}\right)^{20}=\left(\dfrac{3}{10}^4\right)^5=\left(\dfrac{3}{10000}\right)^5\)
Vì \(\dfrac{1}{1000}>\dfrac{3}{10000}\) nên \(\left(\dfrac{1}{10}\right)^{15}>\left(\dfrac{3}{10}\right)^{20}\)
\(\left(\frac{1}{5}\right)^{45}=\frac{1}{5^{45}}\)
\(\left(\frac{-1}{2}\right)^{60}=\frac{1}{2^{60}}\)
Thấy 545=(53)15
260=(24)15
5^3=125>2^4=16
=> 5^45<2^60
=> 1/5^45>1/2^60
Ta có \(\left(17^5\right)^2=17^{10}\)
Vì \(17^{10}=17^{10}\Rightarrow\left(17^5\right)^2=17^{10}\)
\(2^{60}=\left(2^3\right)^{20}=8^{20}\)
Vì \(8^{20}>4^{20}\Rightarrow2^{60}>4^{20}\)
\(5^{45}=\left(5^3\right)^{15}=125^{15}\)
Vì \(125^{15}>25^{15}\Rightarrow5^{45}>25^{15}\)
a, Ta có : \(\left(17^5\right)^2=17^{10}\)
Vì \(17^{10}=17^{10}\Rightarrow\left(17^5\right)^2=17^{10}\)
b, Ta có \(2^{60}=\left(2^3\right)^{20}=8^{20}\)
Vì \(8^{20}>4^{20}\Rightarrow2^{60}>4^{20}\)
c, Ta có : \(5^{45}=\left(5^3\right)^{15}=125^5\)
Vì \(125^5>25^{15}\Rightarrow5^{45}>25^{15}\)