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a, \(a^3.a^5.a^8=a^{16}\)
b, \(4^5.16^3.32=\left(2^2\right)^5.\left(2^4\right)^3.2^5=2^{10}.2^{12}.2^5=2^{27}\)
c,\(9^4.27^3.3^8=\left(3^2\right)^4.\left(3^3\right)^3.3^8=3^8.3^9.3^8=3^{25}\)
d,\(72^5:36^5=\left(72:36\right)^5=2^5\)
e, \(9^{10}:27^5=\left(3^2\right)^{10}:\left(3^3\right)^5=3^{20}:3^{15}=3^5\)
a)a^3.a^5.a^8=a^16
b) 4^5.16^3.32=(2^2)^5.(2^4)^3.2^5=2^10.2^12.2^5=27
c) 9^4.27^3.3^8=(3^2)^4.(3^3)^3.3^8=3^8.3^9.3^8=3^25
a) am : an = am-n
b) 12018 : 12015 = 12018-2015 = 13
c) 25 : 25 = 25-5 = 20
B) 273 : 33 = 19683 : 27 = 729
153 : 53 = 3375 : 125 = 27
A
a)\(a^m:a^n=a^{m-n}\)
b)\(1^{2018}:1^{2015}=1\)( cái này dễ mà cũng phải hỏi )
c)\(2^5:2^5=2^0=1\)
A= 82 . 324 = (23)2 . (25)4 = 26.220 = 226
\(B=27^3.9^4.81^2\)
\(=\left(3^3\right)^3.\left(3^2\right)^4.\left(3^4\right)^2\)
\(=3^9.3^8.3^8\)
\(=3^{25}\)
A) \(2^{300}=\left(2^3\right)^{100}=8^{100}\)
\(3^{200}=\left(3^2\right)^{100}=9^{100}\)
do \(8^{100}< 9^{100}=>A< B\)
B) \(27^5=\left(3^3\right)^5=3^{15}\)
\(243^3=\left(3^5\right)^3=3^{15}\)
=> \(27^5=243^3\)
a) A = 2 + 23+25+...+249
=> 22.A = 23+25+27+...+251
22.A - A = 251-2
3A=251-2
\(A=\frac{2^{51}-2}{3}\)
b) B = 31-35+39-313+...-381
=> 34.B = 35 - 39+ 313 - 317+...-385
=> 34.B - B = -385-31
81B - B = -385-31
\(B=\frac{-3^{85}-3^1}{80}\)
c) C = -4-42-43-44-...-4100
=> 4C = -42-43-44-45-...-4101
=> 4C - C = -4101+4
3C = -4101+4
\(C=\frac{-4^{101}+4}{3}\)
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)Đặt A=\(3+3^2+3^3+...+3^{2018}\)
3A=\(3^2+3^3+3^4+...+3^{2019}\)
3A-A hay 2A=\(3^{2019}-3\)
\(\Rightarrow\)A=\(\left(3^{2019}-3\right):2\)
b)\(81.\left[27+9^{15}.\left(3^5+3^{32}\right)\right]\)
\(=3^4.\left[3^3+3^{30}.\left(3^5+3^{32}\right)\right]\)
Học tốt nha!!!