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Ta có : \(5^7.25^7=5^7.\left(5^2\right)^7=5^7.5^{14}=5^{21}\)
\(625^6=\left(5^4\right)^6=5^{24}\)
mà 21 < 24
\(\Rightarrow5^{21}< 5^{24}\)
\(\Rightarrow5^7.25^7< 625^6\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1,\\ a,\Leftrightarrow4^{5-x}=4^2\Leftrightarrow5-x=2\Leftrightarrow x=3\\ b,\Leftrightarrow\left[{}\begin{matrix}x-1=5\\x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-4\end{matrix}\right.\\ c,\Leftrightarrow2x+1=3\Leftrightarrow x=2\\ 2,\\ a,3^{100}=\left(3^2\right)^{50}=9^{50}\\ b,2^{98}=\left(2^2\right)^{49}=4^{49}< 9^{49}\\ c,5^{30}=5^{29}\cdot5< 6\cdot5^{29}\\ d,3^{30}=\left(3^3\right)^{10}=27^{10}>8^{10}\\ 4,\\ a,\Leftrightarrow5\left(x-10\right)=10\\ \Leftrightarrow x-10=2\Leftrightarrow x=12\\ b,\Leftrightarrow3\left(70-x\right)+5=92\\ \Leftrightarrow3\left(70-x\right)=87\\ \Leftrightarrow70-x=29\\ \Leftrightarrow x=41\\ c,\Leftrightarrow16+x-5=315-230=85\\ \Leftrightarrow x=74\\ d,\Leftrightarrow2^x-5+74=707:\left(16-9\right)=707:7=101\\ \Leftrightarrow2^x=32=2^5\\ \Leftrightarrow x=5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Ta có:
\(A=-3\cdot7\cdot\left(-2\right)\cdot\left(-13\right)\)
\(A=-21\cdot26\)
\(A=-546\)
\(B=-1\cdot\left(-2\right)\cdot\left(-3\right)\cdot\left(-4\right)\cdot5\)
\(B=2\cdot12\cdot5\)
\(B=2\cdot60\)
\(B=120\)
Mà: \(120>-546\)
\(\Rightarrow B>A\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
a) \(\dfrac{-5}{6}\ne\dfrac{10}{-14}\left(\dfrac{10}{-14}=-\dfrac{5}{7}\right).\)
b) \(\dfrac{-15}{-60}\ne\dfrac{-3}{12}\left(\dfrac{-15}{-60}=\dfrac{1}{4}\right).\)
Bài 2:
a) \(\dfrac{20}{-140}=-\dfrac{1}{7}.\)
b) \(\dfrac{4.18}{9.12}=\dfrac{72}{108}=\dfrac{2}{3}.\)
c) \(\dfrac{17.25-17.3}{2.\left(-15\right)}=\dfrac{17.\left(25-3\right)}{-30}=-\dfrac{17.22}{30}=\dfrac{374}{30}=\dfrac{187}{15}.\)
Bài 3:
a) \(\dfrac{-3}{5}< \dfrac{4}{-7}.\)
b) \(\dfrac{-4}{21}>\dfrac{-7}{35}.\)
c) \(\dfrac{-7}{24}>\dfrac{-2}{3}.\)
d) \(\dfrac{-52}{167}< \dfrac{-3}{-4}.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
a)12,5 x (-5/7) + 1,5 x (-5/7)
=-5/7*(12,5+1,5)
=-5/7*14
=-10
b)(-1/4) x (6|2/11) + 3|9/11 x (-1/4)
=-1/4*(68/11+42/11)
=-1/4*10
=-5/2
c tương tự
d)\(\frac{9^8\cdot4^3}{27^4\cdot6^5}=\frac{\left(3^2\right)^8\cdot\left(2^2\right)^3}{\left(3^3\right)^4\cdot\left(2\cdot3\right)^5}=\frac{3^{16}\cdot2^6}{3^{12}\cdot2^5\cdot3^5}=\frac{3^{16}\cdot2^5\cdot2}{3^{16}\cdot3^1\cdot2^5}=\frac{2}{3}\)
Bài 2:
a)Ta có:
2800=(28)100=256100
8200=(82)100=64100
Vì 256100>64100 =>2800>8200
b)Ta có:
1245=(123)15=172815
Vì 62515<172815 =>62515<1245
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 1:
a: \(16^4=2^{16}< 4^{16}\)
c: \(3^{25}=9\cdot3^{23}>8\cdot3^{23}\)
d: \(2^{50}=32^{10}>25^{10}=5^{20}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)
57 . 257 và 6255
Ta có:
57 . 257 = 1257 =( 53 )7 = 53.7 = 521
6255 = ( 54 )5 =54.5 = 520
Vì 521 > 520 => 57 . 257 > 6255
Vậy 57 . 257 > 6255
b) ( 34 )4 và ( 32 )6
Ta có:
( 34 )4 = 34.4 = 316
( 32 )6 = 32.6 = 312
Vì 316 > 312 => ( 34 )4 > ( 32 )6
Vậy ( 34 )4 > ( 32 )6
c) 8 . 24 và 29
Ta có:
8 . 24 = 23 . 24 = 27
Vì 27 < 29 => 8 . 24 < 29
Vậy 8 . 24 < 29
Học tốt!!!