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a: \(=\left\{145-\left[130-10\right]:2\right\}\cdot5\)
\(=\left\{145-60\right\}\cdot5=85\cdot5=425\)
b: \(=100:\left\{250:\left[450-4\cdot125+4\cdot25\right]\right\}\)
\(=\dfrac{100}{250:\left[450-500+100\right]}=\dfrac{100}{250:50}=\dfrac{100}{5}=20\)
c: \(=355-5\cdot\left[64-\left(27-25\right)\right]=355-5\cdot\left[64-2\right]\)
\(=355-310=45\)
a) 3 . 52 + 15 . 22 - 26 : 2
= 3 . 25 + 15 . 4 - 26 : 2
= 75 + 60 - 13
= 135 - 13
= 122
b) 53 . 2 - 100 : 4 + 23 . 5
= 125 . 2 - 100 : 4 + 8 . 5
= 250 - 25 + 40
= 225 + 40
= 265
c) (519 : 517 + 3 ) : 7
= (52 + 3) : 7
= (25 + 3) : 7
= 28 : 7
= 4
d) 79: 77 - 32 + 23 . 52
= 72 - 32 + 23 . 52
= 49 - 9 + 8 . 25
= 40 + 200
= 240
e) 791 : 789 + 5 . 52 - 124
= 72 + 5 . 25 - 124
= 49 + 125 - 124
= 174 - 124
= 50
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: =5-78*32
=5-2496
=-2491
b: \(=6\left(9-6\right)=6\cdot3=18\)
c: \(=46\cdot\dfrac{\left(123-42\right)}{81}=46\)
d: \(=181+3-84+8\cdot25\)
=100+200
=300
e: \(=64\cdot35+140\cdot84-1=2240-1+11760\)
=14000-1
=13999
f: \(=3^3+25\cdot8-1=26+200=226\)
g: \(=3+2^4+1=16+4=20\)
h: \(=36:4\cdot3+2\cdot25-1=27+50-1=27+49=76\)
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 = 2^3 + 2^4+ 2^5+ 2^6 + 2^7 + ... + 2^90
2A = 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + .... + 2^90 + 2^100
2A - A = ( 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + .... + 2^90 + 2^100 ) - ( 2^3 + 2^4+ 2^5+ 2^6 + 2^7 + ... + 2^90 )
A = 2^100 - 2^3
B = 1 + 5 + 5^2 + 5^3 + 5^4 + .... + 5^50
5B = 5 + 5^2 + 5^3 + 5^4 + 5^5 + .... + 5^50 + 5^51
5B - B = ( 5 + 5^2 + 5^3 + 5^4 + 5^5 + .... + 5^50 + 5^51 ) - ( 1 + 5 + 5^2 + 5^3 + 5^4 + .... + 5^50 )
4B = 5^51 - 1
B = 5^51 - 1 / 4