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1.
a, 5.125.625
= 5.53.54
= 51+3+4 = 58
b, 10.100.1000 = 10.102.103 = 106
\(c,8^4.16^5.32=\left(2^3\right)^4.\left(2^4\right)^5.2^5=2^{12}.2^{20}.2^5=2^{37}\)
\(d,27^4.81^{10}=\left(3^3\right)^4.\left(3^4\right)^{10}=3^{12}.3^{40}=3^{52}\)
2,
a, \(12^7:6^7=\left(12:6\right)^7=2^7\)
\(b,27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^{15-12}=3^3\)
\(c,18^3:9^3=\left(18:9\right)^3=2^3\)
\(d,125^3:2=\frac{125^3}{2}\)
Phần d bài 2 nó kiểu gì ý
57 :
a , 5 . 25 . 125 = 5 . 52 . 53 = 51+2+3 = 56
b , 10 . 100 . 1000 = 10 . 102 . 103 = 101+2+3 = 106
c , 84 . 165 . 32 = ( 23 )4 . ( 24 )5 . 25 = 212 . 220 . 25 = 212+20+5 = 237
d , 274 . 8110 = ( 33 )4 . ( 34 )10 = 312 . 340 = 312+40 = 352
62 : a , 127 : 67 = ( 6 . 2 )7 : 67 = 67 . 27 : 67 = 67 : 67 . 27 = 1 . 27 = 27 = 128
b , 275 : 813 = ( 33 )5 : ( 34 )3 = 315 : 312 = 315-12 = 33 = 27
c , 183 : 93 = ( 2 . 9 )3 : 93 = 23 . 93 : 93 = 23 . 1 = 23 = 8
d , 1253 : 2 = ( 53 )3 : 2 = 59 : 2 = 1953125 : 2 = 976562,5
\(a.13-18-\left(-42\right)-15\)
\(=-5-\left(-42\right)-15\)
\(=37-15\)
\(=22\)
\(b.\left(-8\right)^3:\left(-8^2\right)-8\)
\(=-8-8\)
\(=-16\)
\(A=8^{2017}-8^{2016}+...+8-1\)
\(8A=8^{2018}-8^{2017}+...+8^2-8\)
\(8A+A=\left(8^{2018}-8^{2017}+...+8^2-8\right)+\left(8^{2017}-8^{2016}+...+8-1\right)\)
\(9A=8^{2018}-8^{2017}+...+8^2-8+8^{2017}-8^{2016}+...+8-1\)
\(9A=8^{2018}-1\)
\(9A+1=8^{2018}-1+1=8^{2018}=8^{n+2006}\)
=>n+2006=2018
=>n=12
\(a,\left(-14\right)\cdot\left(-125\right)\cdot\left(+3\right)\cdot\left(-8\right)\\ =\left[\left(-125\right)\cdot\left(-8\right)\right]\cdot\left[3\cdot\left(-14\right)\right]\\ =1000\cdot\left(-42\right)\\ =-42000\)
Xem lại đề câu b nhé
\(D=2^{100}-2^{99}-2^{98}-...-2^2-2-1\\ =2^{100}-\left(2^{99}+2^{98}+...+2^2+2+1\right)\\ \text{Đặt }G=2^{99}+2^{98}+...+2^2+2+1\\ 2G=2^{100}+2^{99}+...+2^3+2^2+2\\ 2G-G=\left(2^{100}+2^{99}+...+2^3+2^2+2\right)-\left(2^{99}+2^{98}+...+2^2+2+1\right)\\ G=2^{100}-1\\ D=2^{100}-G\\ =2^{100}-\left(2^{100}-1\right)\\ =2^{100}-2^{100}+1\\ =1\)
\(a,\frac{8^{2017}-8^{2015}}{8^{2014}.8}\)
\(=\frac{8^{2015}.\left(8^2-1\right)}{8^{2015}}\)
\(=64-1\)
\(=63\)
\(b,\frac{2^8+8^3}{2^5.2^3}\)
\(=\frac{2^8+\left(2^3\right)^3}{2^8}\)
\(=\frac{2^8+2^9}{2^8}\)
\(=\frac{2^8.\left(1+2\right)}{2^8}\)
\(=3\)
Học tốt
82017 - 82015 = 82015(82 - 1) = 82015.63
82014.8 = 82014+1 = 82015
=> \(\frac{8^{2017}-8^{2015}}{8^{2014}\cdot8}=\frac{8^{2015}\cdot63}{8^{2015}}=63\)
28 + 83 = 28 + (23)3 = 28 + 29 = 28(1 + 2) = 28.3
25.23 = 25+3 = 28
=> \(\frac{2^8+8^3}{2^5\cdot2^3}=\frac{2^8\cdot3}{2^8}=3\)