5 mũ 20 - 5 mũ 15 / 5 mũ 16 + 5 mũ 18
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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
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) (495 . 716) : (718.76)
=((72)5.716) :724
=(710.716) :724
=726 : 724=72=49
b) (416.820 ) : (214.3215)
=((22)16.(23)20) : (214.(25)15
=(232.260) : (214.275)
=292 : 289=23=8
\(5^{12}.7-5^{11}.10\)
\(=5^{11}.\left(5.7-10\right)\)
\(=5^{11}.25\)
\(=5^{11}.5^2\)
\(=5^{13}\)
\(2^{20}.15+2^{20}.85\)
\(=2^{20}.5\left(3+17\right)\)
\(=2^{20}.100\)
\(=104857600\)
\(125^3:25^4\)
\(=\left(5^3\right)^3:\left(5^2\right)^4\)
\(=5^9:5^8\)
\(=5\)
\(24^4:3^4-32^{12}:16^{12}\)
\(=\left(24:3\right)^4-\left(32:16\right)^{12}\)
\(=8^4-2^{12}\)
\(=0\)
\(\left(37+18\right).\left\{3250-15^2.\left[\left(4^4-2^5\right):16\right]\right\}\)
\(=55.\left\{3250-225.\left[\left(256-32\right):16\right]\right\}\)
\(=55.\left\{3250-225.14\right\}\)
\(=55.\left\{3250-3150\right\}=55.100=5500\)
( 37 + 18 ) . { 3250 - 152 . [ 44 - 25 ) : 16 ] }
= 55 . { 3250 - 225 . ( 256 - 32 ) : 16 ] }
= 55 . { 3250 - 225 . 224 : 16 }
= 55 . { 3250 - 3150 }
= 55 . 100
= 5500.
\(\dfrac{5^{20}-5^{15}}{5^{16}+5^{18}}\)
\(=\dfrac{5^{15}\cdot\left(5^5-1\right)}{5^{16}\cdot\left(1+5^2\right)}\)
\(=\dfrac{3125-1}{5\cdot\left(1+25\right)}\)
\(=\dfrac{3124}{5\cdot26}\)
\(=\dfrac{1562}{65}\)
\(\dfrac{5^{20}-5^{15}}{5^{16}+5^{18}}\\ =\dfrac{5^{15}\left(5^5-1\right)}{5^{16}\left(1+5^2\right)}\\ =\dfrac{5^5-1}{5\left(1+25\right)}\\ =\dfrac{3125-1}{5\cdot26}\\ =\dfrac{3124}{130}\\ =\dfrac{1562}{65}\)