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\(a,\dfrac{7}{35},\dfrac{18}{54},\dfrac{-15}{125},\dfrac{-4}{25}\)
Các thừa số đã tối giản : \(\dfrac{-4}{25}\)
\(\dfrac{7}{35}=\dfrac{7:7}{35:7}=\dfrac{1}{5}\) , \(\dfrac{18}{54}=\dfrac{18:18}{54:18}=\dfrac{1}{3}\)
\(\dfrac{-15}{125}=\dfrac{-15:5}{125:5}=\dfrac{-3}{25}\)
\(b,\dfrac{27}{45},\dfrac{21}{28},\dfrac{8}{14},\dfrac{18}{-60},\dfrac{-270}{360}\)
Các thừa số đã tối giản là : ko có
\(\dfrac{27}{45}=\dfrac{27:9}{45:9}=\dfrac{3}{5}\) , \(\dfrac{21}{28}=\dfrac{21:7}{28:7}=\dfrac{3}{4}\)
\(\dfrac{8}{14}\)\(=\dfrac{8:2}{14:2}=\dfrac{4}{7}\) , \(\dfrac{18}{-60}=\dfrac{18:6}{-60:6}=\dfrac{3}{-10}=\dfrac{-3}{10}\)
\(\dfrac{-270}{360}=\dfrac{-270:90}{360:90}=\dfrac{-3}{4}\)
\(c,\dfrac{3.4+3.7}{6.5+9}\) = \(\dfrac{3.\left(4+7\right)}{30+9}\) = \(\dfrac{3.11}{39}\) = \(\dfrac{3.11}{3.13}=\dfrac{11}{13}\)
\(\dfrac{-63}{81},\dfrac{9.6}{9.35},\dfrac{7.2+8}{2.14.5}\)
Các p/s đã tối giản : ko có
\(\dfrac{-63}{81}=\dfrac{-63:9}{81:9}=\dfrac{-7}{9}\) , \(\dfrac{9.6}{9.35}=\dfrac{6}{35}\)
\(\dfrac{7.2+8}{2.14.5}=\dfrac{14+8}{28.5}=\dfrac{22}{140}=\dfrac{11}{70}\)
a) Có: \(3+3^2+3^3+3^4+...+3^{99}\\ =\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{97}+3^{98}+3^{99}\right)\\ =\left(3+3^2+3^3\right)+3^3\left(3+3^2+3^3\right)+...+3^{97}\left(3+3^2+3^3\right)\\ =39+3^3\cdot39+...+3^{97}\cdot39\\ =13\cdot3+3^3\cdot13\cdot3+...+3^{97}\cdot13\cdot3\\ =13\left(3+3^4+...+3^{98}\right)⋮13\left(đpcm\right)\)
b) Có: \(81^7-27^9-9^{13}\\ =\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\\ =3^{28}-3^{27}-3^{26}\\ =3^{26}\left(3^2-3-1\right)\\ =3^{24}\cdot\left(3^2\cdot5\right)\\ =3^{24}\cdot45⋮45\left(đpcm\right)\)
c) Có: \(24^{54}\cdot54^{24}\cdot2^{10}\\ =\left(2^3\cdot3\right)^{54}\cdot\left(2\cdot3^3\right)^{24}\cdot2^{10}\\ =2^{162}\cdot3^{54}\cdot2^{24}\cdot3^{72}\cdot2^{10}\\ =2^{196}\cdot3^{126}\\ =2^7\cdot\left(2^{189}\cdot3^{126}\right)\\ =2^7\cdot\left[\left(2^3\right)^{63}\cdot\left(3^2\right)^{63}\right]\\ =2^7\left(8^{63}\cdot9^{63}\right)\\ =2^7\cdot72^{63}⋮72^{63}\left(đpcm\right)\)
a) ta có: 3 + 32 + 33 + 34 + ... + 399
= (3 + 32 + 33) + (34 + 35 +36) + ... + (397 + 398 + 399)
= 3(1 + 3 + 32) + 34(1 + 3 + 3) + ... + 396(1 + 3 + 3)
= 3.13 + 34.13 + ... + 396.13
= 13(3 + 34 + ... + 396) ⋮ 13
vậy (3 + 32 + 33 + 34 + ... + 399) ⋮ 13
b) ta có: 817 - 279 - 913
= (34)7 - (33)9 - (32)13
= 328 - 327 - 326
= 326(32 - 3 - 1)
= 326 . 5 = 324 (9.5) = 324 . 45 ⋮ 45
Vậy (817 - 279 - 913) ⋮ 45
c) ta có: 2454.5424.210
= (23.3)54 . (2.33)24 . 210
= 2162 . 354 . 224 . 372 . 210
= 2196 . 3126
= (2193.3124).(23.32)
= (2193.3124).72 ⋮ 72
vậy (2454.5424.210) ⋮ 72
\(a,36.19+36.81\)
\(=36.\left(19+81\right)\)
\(=36.100\)
\(=3600\)
\(b,8.12.125.5\)
\(=\left(125.8\right)\left(12.5\right)\)
\(=1000.60\)
\(=60000\)
\(c,\)chịu
c,7 x 9 + 14 x 27 + 21 x 36 / 21 x 27 + 42 x 81 + 63 x 108
7 x 9 + 14 x 27 + 21 x 36 / 7 x 3 x 9 x 3 + 14 x 3 x 27 x 3 + 21 x 3 x 36 x 3
1 / 3 x 3 + 3 x 3 + 3 x 3
1 / 9 + 9 + 9
1 / 27
a)\(\hept{\begin{cases}x⋮18\\x⋮24\end{cases}\Rightarrow x\in BC\left(18,24\right)}\)
Ta có
\(18=3^2.2\)
\(24=2^3.3\)
\(\Rightarrow BCNN\left(18,24\right)=3^2.2^3=72\)
\(\Rightarrow BC\left(18,24\right)=\left\{0;72;144;216;...\right\}\)
Mà \(100< x< 150\)
\(\Rightarrow x=144\)
b)\(\hept{\begin{cases}126⋮x\\36⋮x\end{cases}\Rightarrow x\inƯC\left(126,36\right)}\)
Ta có
\(126=2.3^2.7\)
\(36=2^2.3^2\)
\(\RightarrowƯCLN\left(126,36\right)=2.3^2=18\)
\(\RightarrowƯC\left(126,36\right)=\left\{1;2;3;6;9;18\right\}\)
Mà \(x>10\)
\(\Rightarrow x=18\)
c)\(\hept{\begin{cases}48⋮x\\32⋮x\end{cases}\Rightarrow x\inƯC\left(48,32\right)}\)
Mà x lớn nhất \(\Rightarrow x=ƯCLN\left(48,32\right)\)
Ta có
\(48=2^4.3\)
\(32=2^5\)
\(\RightarrowƯCLN\left(48,32\right)=2^4=16\)
Vậy \(x=16\)
d)\(\hept{\begin{cases}x⋮18\\x⋮24\\x⋮54\end{cases}\Rightarrow x\in BC\left(18,24,54\right)}\)
Mà x nhỏ nhất khác 0 \(\Rightarrow x=BCNN\left(18,24,54\right)\)
Ta có
\(18=2.3^2\)
\(24=2^3.3\)
\(54=2.3^3\)
\(\Rightarrow BCNN\left(18,24,54\right)=2^3.3^3=216\)
Vậy \(x=216\)
d) 4x.4 + 4x = 320
4x.(4+1) = 320
4x.5 = 320
4x = 320 : 5
4x = 64 = 43
=> x = 3
e) 5x+3+5x = 630
5x.53+5x = 630
5x.(53+1) = 630
5x.126 = 630
5x = 630 : 126
5x = 5 =51
=> x = 1
g) 9x=274
(32)x = (33)4
32x = 312
=> 2x = 12
x = 6
a) 3x -18 = 0
3x = 18
=> không tìm được x
b) 4.5x =100
5x =100 : 4
5x = 25 = 52
=> x = 2
c) 3x:32=94
3x-2 = (32)4 =38
=> x- 2 = 8
x = 10
a) \(x\in\left\{34;51;68;85;102;119;136\right\}\)
b) \(x\in\left\{18;36;54;72\right\}\)
c) \(x\in\left\{12;18\right\}\)
d) \(x\in\left\{1;2;3;5;6\right\}\)
e) \(x\in\left\{3;4;6;10\right\}\)
k) \(x\in\left\{1;2;4;11\right\}\)
Đáp án là B
Ta có:
⇒ x ∈ {0; 9; 18; 27; 36; 45; 54}