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1) = 2750 - 1229 + 2570 + 438 + 29 + 438
= (2750 + 2750) - (1229 - 29) + (438 + 438)
= 5500 - 1200 + 876
= 5176
2) = 38.9 + 17.9 - 35.9 - 11.35
= (38+17-35).9 - 11.35
= 20.9 - 11.35
= 180 - 385
= -205
3) = 500 - \(\left\{5.\left[409-\left(24-21\right)^2\right]+1000\right\}\) : 15
= 500 - \(\left\{5.\left[409-9\right]+1000\right\}:15\)
= 500 - \(\left\{5.400+1000\right\}:15\)
= 500 - (2000 + 1000) : 15
= 500 - 200
= 300
a) 32-6.(8-23)+18
= 32 - 6 . (8 - 8) +18
=32 - 0 +18
= 50
b) (3.5-9)3.(1+2.3)2+42
= (15-9 )3. (1+6)2 + 4 2
= 63 . 7 2 + 42
= 216 x 49 + 16
= 10584 + 16
=10600
c) 9234:[3.3.(1+83)]
= 9234 : [ 3.3.93]
= 9234 : [ 3.3 . 729]
= 9234 :6561
= 1,407407407
d) 76- {2.[2.52-(31-2.3)]}+3.25
= 76 - { 2. [ 2.52 - ( 31 - 6)]} + 3.25
= 76 - { 2 . [ 2. 52 - 25 ]} + 3 .25
= 76 - { 2 . [2. 25 - 25]} + 3.25
= 76 - { 2.[ 50 - 25 ]} + 3.25
= 76 - { 2. 25} + 3 . 25
= 76 - 50 + 3. 25
= 76 - 50 + 75
= 101
\(=\frac{\left(2^2\right)^5.\left(3^3\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(2.3\right)^8.2.10}\)
\(=\frac{2^{10}.3^{12}-2.2^9.3^9}{2^{10}.3^8+2^8.2^2.3^8.5}\)
\(=\frac{2^{10}.\left(3^{12}-3^9\right)}{2^{10}.3^8.\left(1+5\right)}\)
\(=\frac{3^9.\left(3^3-1\right)}{3^8.3.2}\)
\(=\frac{3^9.26}{3^9.2}\)
\(=\frac{26}{2}=13\)
Bài 1 :
a, \(\left(x^2-29\right)^3=343\)
=> \(\left(x^2-29\right)^3=7^3\)
=> \(x^2-29=7\)
=> \(x^2=7+29=36\)
=> \(\orbr{\begin{cases}x=6\\x=-6\end{cases}}\)
Do x là số tự nhiên => x = 6
b, \(2^{x+2}+2^{x-1}+2^{x-2}=152\)
=> \(2^x.2^2+2^x:2^1+2^x:2^2=152\)
=> \(2^x.2^2+2^x.\frac{1}{2}+2^x.\frac{1}{4}=152\)
=> \(2^x.\left(2^2+\frac{1}{2}+\frac{1}{4}\right)=152\)
=> \(2^x.\frac{19}{4}=152\)
=> \(2^x=32\)
=> \(2^x=2^5\)
=> x = 5
Bài 2 :
a, \(\left(2^9.76+2^{10}.35\right).3=2^{10}.38+2^{10}.35=2^{10}\left(38+35\right).3=2^{10}.73.3=1024.3.73=224256\)
b, \(\frac{\left(2^9.76+2^{10}.35\right).3}{2^8.438}=\frac{2^{10}.73.3}{2^9.219}=\frac{2^{10}.219}{2^9.219}=2\)
B = 22 + 23 + 24 + ... + 210
\(\Rightarrow\)2B = 23 + 24 + 25 + ... + 211
\(\Rightarrow\)2B - B = (23 + 24 + 25 + ... + 211) - (22 + 23 + 24 + ... + 210)
\(\Rightarrow\)B = 211 - 22
\(\Rightarrow\)B = 2048 - 4 = 2044
Vì 2044\(⋮\)7 nên B\(⋮\)7
\(\Rightarrow\)ĐPCM