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\(a,4^{72}v\text{à}8^{48}\)
TA CÓ:\(4^{72}=\left(2^2\right)^{72}=2^{144}\)
\(8^{48}=\left(2^3\right)^{48}=2^{144}\)
\(\Rightarrow4^{72}=8^{48}\)
\(b,5^{127}v\text{à}2^{254}\)
TA CÓ:\(2^{252}2^{2\times127}=\left(2^2\right)^{127}=4^{127}\)
\(5^{127}>4^{127}\left(v\text{ì5>4}\right)\)\(5^{127}>4^{127}\left(v\text{ì}5>4\right)\)
\(\Rightarrow5^{127}>2^{254}\)
a) Ta có : 472 = 43.24 = (43)24 = 6424
848 = 82.24 = (82)24 = 6424
Ta thấy : 6424 = 6424 => 472 = 848
b) Ta có : 2254 = 22.127 = (22)127 = 4127
Vì 5 > 4 => 5127 > 2254
Ta có
\(\frac{13}{27}:\frac{13}{27}=1\)
\(\frac{7}{15}:\frac{13}{27}=\frac{63}{65}\)
Mặt khác \(\frac{63}{65}< 1\)
\(\Rightarrow\frac{13}{27}:\frac{13}{27}>\frac{7}{15}:\frac{23}{27}\)
\(\Rightarrow\frac{13}{27}:\frac{13}{27}\times\frac{13}{27}>\frac{7}{15}:\frac{23}{27}\times\frac{13}{27}\)
\(\Rightarrow\frac{13}{27}>\frac{7}{15}\)
Bài 2:
1: \(2A=2+2^2+...+2^{2011}\)
=>\(A=2^{2011}-1>B\)
2: \(A=\left(2010-1\right)\left(2010+1\right)=2010^2-1< B\)
3: \(A=1000^{10}\)
\(B=2^{100}=1024^{10}\)
mà 1000<1024
nên A<B
5: \(A=3^{450}=27^{150}\)
\(B=5^{300}=25^{150}\)
mà 27>25
nên A>B
a) \(\frac{3}{-4}=\frac{-3}{4};\frac{-1}{-4}=\frac{1}{4}\)
Vì - 3 < 1 nên \(\frac{-3}{4}< \frac{1}{4}\)
hay \(\frac{3}{-4}< \frac{-1}{-4}\)
Quy đồng mẫu ta được:
15/17=15.27/17.27=405/459
25/27=25.17/27.27=425/459
⇒405/459<425/459⇒15/17<25/27
a, \(-2,5\%-\left[1-\left(\frac{2}{3}\right)^2\right]+\left(1-\frac{4}{9}\right)\\ =\frac{-1}{40}-\left[1-\frac{4}{9}\right]+\left(1-\frac{4}{9}\right)\\ =\frac{-1}{40}+\left[\left(1-\frac{4}{9}\right)-\left(1-\frac{4}{9}\right)\right]\\ =\frac{-1}{40}+0\\ =\frac{-1}{40}\)
b, \(5\frac{1}{2}-14\frac{3}{7}:\frac{9}{13}-3\frac{4}{7}:\frac{9}{13}\\ =5\frac{1}{2}-\left(14\frac{3}{7}:\frac{9}{13}+3\frac{4}{7}:\frac{9}{13}\right)\\ =5\frac{1}{2}-\left[\left(14\frac{3}{7}+3\frac{4}{7}\right):\frac{9}{13}\right]\\ =5\frac{1}{2}-\left(18:\frac{9}{13}\right)\\ =5\frac{1}{2}-\left(18\cdot\frac{13}{9}\right)\\ =\frac{11}{2}-26\\ =\frac{-41}{2}\)
c, \(\left(1+2\frac{1}{4}-3\frac{1}{3}\right):\left(1+3\frac{1}{2}-4\frac{7}{12}\right)\\ =\left(3\frac{1}{4}-3\frac{1}{3}\right):\left(4\frac{1}{2}-4\frac{7}{12}\right)\\ =\frac{-1}{12}:\frac{-1}{12}\\ =1\)
a ) − 5 4 < − 1. b ) 31 8 > 2. c ) 9 14 < 17 7 . d ) 67 60 > 1 10