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2. a) \(3^{200}=\left(3^2\right)^{100}=9^{100}\)
\(2^{300}=\left(2^3\right)^{100}=8^{100}\)
Vì \(9^{100}>8^{100}\Rightarrow3^{200}>2^{300}\)
b) \(71^{50}=\left(71^2\right)^{25}=5041^{25}\)
\(37^{75}=\left(3^3\right)^{25}=27^{25}\)
Vì \(5041^{25}>27^{25}\Rightarrow71^{50}>37^{75}\)
c) \(\frac{201201}{202202}=\frac{201201:1001}{202202:1001}=\frac{201}{202}\)
\(\frac{201201201}{202202202}=\frac{201201201:1001001}{202202202:1001001}=\frac{201}{202}\)
Vì \(\frac{201}{202}=\frac{201}{202}\Rightarrow\frac{201201}{202202}=\frac{201201201}{202202202}\)
a)\(\frac{7}{13}.\frac{7}{15}-\frac{5}{12}.\frac{21}{39}+\frac{49}{21}.\frac{8}{15}\)
=\(\frac{7}{13}.\frac{7}{15}-\frac{5}{12}.\frac{7}{13}+\frac{7}{13}.\frac{8}{15}\)
=\(\frac{7}{13}.\left(\frac{7}{15}-\frac{5}{12}-\frac{8}{15}\right)\)
=\(\frac{7}{13}.\frac{7}{12}\)
=\(\frac{49}{156}\)
b)\(\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right).\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
=\(a.\left(\frac{3}{6}-\frac{2}{6}-\frac{1}{6}\right)\)
=a . 0
=0
Bài 2
a)Có
\(3^{200}=3^{2.100}=\left(3^2\right)^{100}=9^{100}\)
\(2^{300}=2^{3.100}=\left(2^3\right)^{100}=8^{100}\)
Vì 8<9 =>\(8^{100}< 9^{100}\) =>\(3^{200}>2^{300}\)
a) 125^80 < 25^118
b) 2^91 > 5^35
c) 107^50 < 73^75
d) 54^4 < 21^12
e) 21^15 < 27^5 . 49^8
k cho mk nha
Câu 1 : Tìm số tự nhiên a , biết :
( a + 1 ) + ( a + 2 ) + ( a + 3 ) +...+ ( a + 49 ) + ( a + 50 ) = 2525
(a+a+...+a) +(1+2+3+...+50)=2525
50 SH a
50 . a+(50+1).25=2525
50.a + 1275=2525
50.a=2525-1275
50.a=1250
a=1250:50
=>a=25
TICK ĐI RỒI MIK LÀM TIẾP CHO
So so hang la (50-1):1+1=50(so hang)
(a+a+a+...+a)+(1+2+3+...+50)=2525
(a*50)+(50+1)*50:2=2525
a*50+1275=2525
a*50=2525-1275
a*50=1250
a=1250:50
a=25
Bài 1 câu a:
1/-8 + -5/8
= -1/8 - 5/8
= -6/8
= -3/4
Câu b:
-1/21 + -1/28
= -4/84 - 3/84
= - 7/854
Câu c:
-5/9 + 8/15 + -2/11 + 4/-9 + 7/15
= (8/15+ 7/15) - (5/9 + 4/9) - 2/11
= 1 - 1 - 2/11
= 0 - 2/11
= - 2/11
Câu d:
-25/-75 + 17/34 + 121/- 132
= 1/3 + 1/2 - 11/12
= 4/12 + 6/12 - 11/12
= 10/12 - 11/12
= - 1/12
Bài 2a:
51/23 = 5151/2323 = 515151/232323
\(\frac{5151}{2323}\) = \(\frac{5151:101}{2323:101}\) = \(\frac{51}{23}\) (1)
\(\frac{515151}{232323}\) = \(\frac{515151:10101}{232323:10101}\) = \(\frac{51}{23}\) (2)
Từ (1) và (2) ta có:
\(\frac{51}{23}=\frac{5151}{2323}=\frac{515151}{232323}\) (đpcm)