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\(S=\frac{2^2}{2^2-1}\times\frac{3^2}{3^2-1}\times...\times\frac{100^2}{100^2-1}\times\frac{101^2}{101^2-1}\)
\(=\frac{\left(2\times3\times4\times...\times101\right)\times\left(2\times3\times4\times...\times101\right)}{\left(1\times2\times3\times...\times100\right)\times\left(3\times4\times5\times...\times102\right)}\)
\(=\frac{101\times2}{1\times102}=\frac{101}{51}\)
\(51\times S=101\)
a) = 53+4+1 = 58
b) = 65-4 = 6
c) = 32+3+4-7 = 32
d) = x4+2+1 = x7
e) = 812+10+3 = 825
1. \(5^3.5^4.5=5^{3+4+1}=5^8\)
2. \(6^5:\left(6^3.6\right)=6^5:\left(6^{3+1}\right)=6^5:6^4=6^{5-4}=6^1\)
3. \(\left(3^2.3^3.3^4\right):3^7=\left(3^{2+3+4}\right):3^7=3^9:3^7=3^{9-7}=3^2\)
4. \(x^4.x^2.x=x^{4+2+1}=x^7\)
5. \(\left(8^{12}.8^{10}\right).8^3=8^{12+10+3}=8^{25}\)
213 . 45 . 82=213.(22)5.(23)2=213.210.26=213+10+6=219
1006 . 10004 . 100003=(102)6.(103)4.(104)3=1012.1012.1012=1012+12+12=1036
36 9 : 189=(36:18)9=29
245 : 65 . 88=(24:6)5.88=45.88=(22)5.(23)8=210.224=210+24=234
515 . 1253 : 625=515.(53)3.54=515.59.54=515+9+4=528
282014 : 72014 : 60=(28:7)2014 : 1=42014:1=42014
24 . 55 + 52 . 53=24.55+52+3=24.55+55=(24+1).55=25.55=52.55=52+5=57
7 . 39 + 310 + 51 . 38=7.3.38 + 32.38 + 51 . 38=21.38 + 9.38 + 51 . 38=(21+9+51).38=81.38=34.38=34+8=312
a: 2/9-4/9=-2/9
b: 5/7-4/14=5/7-2/7=3/7
c: -2-5/8=-16/8-5/8=-21/8
d: =6/13+14/39=18/39+14/39=32/39
e: =4/5+4/18=72/90+20/90=92/90=46/45
f: =5/30-12/30=-7/30
g: =-63/63=-1
h: =4/13x26=4x2=8
a: 2/9-4/9=-2/9
b: 5/7 - 4/14 = 5/7 - 2/7 = 3/7
c: -2 - 5/8 = - 16/8 - 5/8 = - 21/8
d: = 6/13 + 14/39 = 18/39 + 14/39 = 32/39
e: = 4/5 + 4/18 = 72/90 + 20/90 = 92/90 = 46/45
f: = 5/30 - 12/30 = -7/30
g: = - 63/63 = -1
h: = 4/13 . 26 =4 . 2 = 8
a) 2(4x-8)-7(3+x)=|-4|.(3-2)
8x-16-21-7x=4
8x-7x=4+16+21
x=41
Vậy x=41
b) 8(x-|-7|)-6(x-2)=|-8|.6-50
8x-56-6x+12=8.6-50
8x-6x=48-50+56-12
2x=42
x=42:2
x=21
Vậy x=21
c) -7(5-x)-2(x-10)=15
-35+7x-2x+20=15
7x-2x=15+35-20
5x=30
x=30:5
x=6
Vậy x=6
d) 4(x-1)-3(x-2)=-|-5|
4x-4-3x+6=-5
4x-3x=-5+4-6
x=-7
Vậy x=-7
e) -4(x+1)+(89x-3)=24
-4x-4+89x-3=24
-4x+89x=24+4+3
85x=31
x=31/85
f) 5(x-30)-2(x+6)=9
5x-150-2x-12=9
5x-2x=9+150+12
3x=171
x=171:3
x=57
Vậy x=57
g) -3(x-5)+6(x+2)=9
-3x+15+6x+12=9
-3x+6x=9-15-12
3x=-18
x=-18:3
x=-6
Vậy x=-6
h) 7(x-9)-5(6-x)=-6+11x
7x-63-30+5x=-6+11x
7x+5x-11x=-6+62+30
x=86
Vậy x=86
k) 10(x-7)-8(x+5)=6.(-5)+24
10x-70-8x-40=-30+24
10x-8x=-30+24+70+40
2x=104
x=104:2
x=52
Vậy x=52
356/71 nha bạn