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a,\(5^3.2-100:4+2^3.5\)
= 125 . 2 - 25 + 8 . 5
= 250 - 25 + 40
= 265
b, \(6^2:9+50.2-3^3.3\)
= 36 : 9 + 100 - 27 . 3
= 4 + 100 - 81
= 23
\(a,\)\(\frac{2^5\times3^{12}\times7^8}{2^7\times3^{10}\times7^9}=\frac{3^2\times\left(2^5\times3^{10}\times7^8\right)}{2^2\times7\times\left(2^5\times3^{10}\times7^8\right)}\)\(=\frac{3^2}{2^2\times7}=\frac{9}{28}\)
\(b,\)Tương tự
\(4^2\cdot120-4^3\cdot17+4^2\cdot34\)
\(=4^2\left(120-4\cdot17+34\right)\)
\(=16\left(120-68+34\right)\)
\(=16\cdot86=1088\)
1. 53 = 5.5.5 = 125
2. 27 = 2.2.2.2.2.2.2 = 128
3. 44 = 4.4.4.4 = 256
4. 73 = 7.7.7 = 343
6. 35 = 243
7. 26 = 64
8. 34 = 81
9. 83 = 512
11. 132 = 169
12. 112 = 121
13. 142 = 196
14. 152 = 225
16. 172 = 289
17. 182 = 324
18. 192 = 361
19. 202 = 400
21. 104 = 10000
22. 105 = 100000
23. 106 = 1000000
24. 107 = 10000000
a) 2^4 * 38 - 2^4 * 37 = 16 * 38 - 16 * 37 = 608 - 592 = 16
b) 4^2 * 444446 - 4^3 * 111111 = 16 * 444446 - 64 * 111111 = 7107136 - 7106944 = 192
c) (2^9 * 3 + 2^9 * 5) / 2^12 = (512 * 3 + 512 * 5) / 4096 = (1536 + 2560) / 4096 = 4096 / 4096 = 1
d) 13^2 - (5^2 * 4 + 2^2 * 15) = 169 - (25 * 4 + 4 * 15) = 169 - (100 + 60) = 169 - 160 = 9
\(a,2^4.38-2^4.37=2^4.\left(38-37\right)=2^4.1=16\\ b,4^2.444446-4^3.111111\\ =4^2.\left(444446-4.111111\right)\\ =4^2.2=16.2=32\\ c,\left(2^9.3+2^9.5\right):2^{12}\\ =2^9.\left(3+5\right):2^{12}=2^9.8:2^{12}=2^9.2^3:2^{12}=2^{9+3-12}=2^0=1\\ d,13^2-\left(5^2.4+2^4.15\right)=13^2-5.4.\left(5+4.3\right)\\ =169-20.17\\ =169-340=-171\)
a, 1+3+5+7= 16=42
b, 1+3+5+7+9+11= 36= 62
c, 13 + 23 + 33 + 43= 1+8+27+64=100=102
d, 13 + 23 + 33 + 43 + 53 = 1+ 8 + 27 + 64 + 125 = 225 = 152
+) 37 x ( 3 + 7 ) = 3^3 + 3^7
- 37 x ( 3 + 7 ) = 370
- 3^3 + 3^7 = 27 + 2187 = 2214
Từ đó, suy ra => SAI
+) 59 x ( 5 + 9 ) = 5^3 + 9^3
- 59 x ( 5 + 9 ) = 826
- 5^3 + 9^3 = 125 + 729 = 854
Từ đó, suy ra => SAI