14 mũ 2 + 2401 . 16 + 233 . 14 mũ 5 + 197 : 14 mũ 2
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a: Ta có: \(\frac{36^{10}\cdot14\cdot126}{35^5\cdot6}\)
\(=\frac{\left(2^2\cdot3^2\right)^{10}\cdot2\cdot7\cdot2\cdot3^2\cdot7}{\left(7\cdot5\right)^5\cdot2\cdot3}\)
\(=\frac{2^{20}\cdot3^{20}\cdot3^2\cdot2^2\cdot7^2}{7^5\cdot5^7\cdot2\cdot3}2^{21}\cdot\frac{3^{21}}{7^3}\)
b: \(\frac{21^2\cdot14\cdot126}{35^5\cdot6}\)
\(=\frac{7^2\cdot3^2\cdot2\cdot7\cdot2\cdot3^2\cdot7}{7^5\cdot5^5\cdot3\cdot2}=\frac{7^4\cdot3^4\cdot2^2}{7^5\cdot5^5\cdot3\cdot2}=\frac{2\cdot3^3}{7\cdot5^5}\)
c: \(\frac{4^9\cdot36+64^4}{100\cdot16^4}\)
\(=\frac{2^{18}\cdot2^2\cdot3^2+\left(2^6\right)^4}{2^2\cdot5^2\cdot\left(2^4\right)^4}=\frac{2^{20}\cdot3^2+2^{24}}{2^2\cdot5^2\cdot2^{16}}\)
\(=\frac{2^{20}\left(3^2+2^4\right)}{2^{18}\cdot5^2}=2^2=4\)
36 mũ 10 . 14 . 126 / 35 mũ 5 . 6 ; 21 mũ 2 . 14 .126 / 35 mũ 5 .6 ; 4 mũ 9 . 36 + 64 mũ 4 / 100 . 16 mũ 4
\(\dfrac{4^9\cdot36+64^4}{100\cdot16^4}=\dfrac{2^{20}\cdot3^2+2^{24}}{2^{18}\cdot5^2}=\dfrac{2^{20}\left(3^2+2^4\right)}{2^{18}\cdot5^2}=4\)
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
\(x^3-2^3=2^5-\left(3^{16}:3^{14}+2^8:2^6\right)\)
\(x^3-8=\)\(32-\left(3^2+2^2\right)\)
\(x^3-8=\)\(32-\left(9+4\right)\)
\(x^3-8=32-13\)
\(x^3-8=19\)
\(x^3\) \(=19+8\)
\(x^3\) \(=27\)
=> \(x=3\)
Vậy \(x=3\)
a) \(4^{13}+4^{14}+4^{15}+4^{16}=4^{13}\left(1+4\right)+4^{14}\left(1+4\right)=4^{13}.5+4^{14}.5=5\left(4^{13}+4^{14}\right)⋮5\Rightarrow dpcm\)
c) \(2^{10}+2^{11}+2^{12}+2^{13}+2^{14}+2^{15}\)
\(=2^{10}\left(1+2+2^2\right)+2^{13}\left(1+2+2^2\right)\)
\(=2^{10}.7+2^{13}.7=7\left(2^{10}+2^{13}\right)⋮7\Rightarrow dpcm\)
Câu c bạn xem lại đê
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
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