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a) 53.252:54
= 53.(52)2:54
= 53.54:54
= 53+4-4
= 53
b) 42.(23)2:128
= (22)2.26:27
= 24.26:27
= 24+6-7
= 23
c) 35.243:(32)3
= 35.35:36
= 35+5-6
= 34
d) 205:55
= (20:5)5
= 45
e) 410:810 (Có chắc không vậy ? Hay là 810:410 ?)
g) 415.530
= 415.(52)15
= 415.2515
= (4.25)15
= 10015
h) 2716.910
= (33)16.(32)10
= 348.320
= 348+20
= 368
a: \(\left(3^2\right)^3=3^6\)
\(\left(3^3\right)^2=3^6\)
\(\left(3^2\right)^5=3^{10}\)
\(9^8=3^{16}\)
\(27^6=3^{18}\)
\(81^{10}=3^{40}\)
b: \(\left(5^3\right)^2=5^6\)
\(\left(5^2\right)^4=5^8\)
\(\left(5^4\right)^3=5^{12}\)
\(25^5=5^{10}\)
\(125^{14}=5^{42}\)
1.
a) \(3^4\times3^5\times3^6=3^{4+5+6}=3^{15}\)
b) \(5^2\times5^4\times5^5\times25=5^2\times5^4\times5^5\times5^2=5^{2+4+5+2}=5^{13}\)
c) \(10^8\div10^3=10^{8-3}=10^5\)
d) \(a^7\div a^2=a^{7-2}=a^5\)
2.
\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)
\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)
\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)
a)\(3.3.3.4.4.4=3^3.4^3=12^3\)
b)\(a.a.a+b.b.b.b=a^3+b^4\)
Chúc hk tốt nha!!!
a, 48.84
= (22)8.(23)4
= 216.212
= 228
b, 415.515
= (4.5)15
= 2015
c, 210.15 + 210.85
= 210.(15 + 85)
= 210.100
=210.(2.5)2
= 212.52
d, 33.92
= 33 . (32)2
= 33.34
= 37
e, 512.7 - 511.10
= 511.(5.7 - 10)
= 511.25
=511.52
=513
f, \(x^1\).\(x^2\).\(x^3\)....\(x^{100}\)
= \(x^{1+2+3+...+100}\)
= \(x^{\left(1+100\right).100:2}\)
= \(x^{5050}\)
8=2^3 ; 20=20^1 ; 60=60^1 ; 90=90^1
16=2^4 ; 27=3^3 ; 81=3^4 ; 100=10^2
\(A=3+3^2+3^3+...+3^{10}\)
=>\(3A=3\left(3+3^2+3^3+...+3^{10}\right)=3^2+3^3+3^4+...+3^{11}\)
=>\(3A-A=\left(3^2+3^3+3^4+...+3^{11}\right)\)\(-\left(3+3^2+3^3+...+3^{10}\right)\)
=>\(2A=3^{11}-3\Rightarrow A=\frac{3^{11}-3}{2}\)