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1. a) 6² : 4 . 3 + 2 . 5²
= 36 : 4 . 3 + 2 . 25
= 9 . 3 + 50
= 27 + 50
= 77
b) 5 . 4² - 32 : 4²
= 5 . 16 - 32 : 16
= 80 - 2
= 78
c) 80 - (4 . 5² - 3 .2³)
= 80 - (4 . 25 - 3 . 8)
= 80 - (100 - 24)
= 80 - 76
= 4
d) 2448 : [119 - (23 - 6)]
= 2448 : (119 - 17)
= 2448 : 102
= 24
e) 23 . 85 + 15 . 23 + 170
= 23 . (85 + 15) + 170
= 23 . 100 + 170
= 2300 + 170
= 2470
f) 3³ . 2 - 5 . 2023⁰ + 36 : 3²
= 27 . 2 - 5 . 1 + 36 : 9
= 54 - 5 + 4
= 53
2. a) 123 - 5.(x + 4) = 38
5.(x + 4) = 123 - 38
5.(x + 4) = 85
x + 4 = 85 : 5
x + 4 = 17
x = 17 - 4
x = 13
b) (3.x - 2⁴) . 7³ = 2 . 7⁴
3x - 16 = 2 . 7⁴ : 7³
3x - 16 = 2 . 7
3x = 14 + 16
3x = 30
x = 30 : 3
x = 10
c) (2600 + 6400) - 3.x = 1200
9000 - 3x = 1200
3x = 9000 - 1200
3x = 7800
x = 7800 : 3
x = 2600
d) [(6.x - 72) : 2 - 84] . 28 = 5628
(6x - 72) : 2 - 84 = 5628 : 28
(6x - 72) : 2 - 84 = 201
(6x - 72) : 2 = 201 + 84
(6x - 72) : 2 = 285
6x - 72 = 285 . 2
6x - 72 = 570
6x = 570 + 72
6x = 642
x = 642 : 6
x = 107
e) 70 - 5(x - 3) = 45
5(x - 3) = 70 - 45
5(x - 3) = 25
x - 3 = 25 : 5
x - 3 = 5
x = 5 + 3
x = 8
f) 10 + 2.x = 4⁷ : 4⁵
10 + 2x = 4²
10 + 2x = 16
2x = 16 - 10
2x = 6
x = 6 : 2
x = 3
g) 2.x - 138 = 2³.2²
2x - 138 = 2⁵
2x - 138 = 32
2x = 32 + 138
2x = 170
x = 170 : 2
x = 85
h) 231 - (x - 6) = 1339 : 13
231 - (x - 6) = 103
x - 6 = 231 - 103
x - 6 = 128
x = 128 + 6
x = 134
`@` `\text {Ans}`
`\downarrow`
`j)`
\(x^{17}\div x^{12}=x^{17-12}=x^5\)
`k)`
\(x^8\div x^5=x^{8-5}=x^3\)
`r)`
\(a^5\div a^5=a^{5-5}=a^0=1\)
`l)`
\(x^4\div x=x^{4-1}=x^3\)
`m)`
\(x^7\div x^6=x^{7-6}=x\)
`n)`
\(x^9\div x^9=x^{9-9}=x^0=1\)
`o)`
\(a^{12}\div a^5=a^{12-5}=a^7\)
`p)`
\(a^8\div a^6=a^{8-6}=a^2\)
`q)`
\(a^{10}\div a^7=a^{10-7}=a^3\)
`r(2),`
\(1024\div4=2^{10}\div2^2=2^8\)
`t)`
\(512\div2^3=2^9\div2^3=2^6\)
Ta có \(\dfrac{1}{1.3}\)+\(\dfrac{1}{3.5}\)+\(\dfrac{1}{5.7}\)+...+\(\dfrac{1}{49.51}\)
=\(\dfrac{2}{2}\).(\(\dfrac{1}{1.3}\)+\(\dfrac{1}{3.5}\)+\(\dfrac{1}{5.7}\)+...+\(\dfrac{1}{49.51}\))
=\(\dfrac{1}{2}\).(\(\dfrac{2}{1.3}\)+\(\dfrac{2}{3.5}\)+\(\dfrac{2}{5.7}\)+...+\(\dfrac{2}{49.50}\))
=\(\dfrac{1}{2}\).(1-\(\dfrac{1}{3}\)+\(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{49}-\dfrac{1}{51}\))
=\(\dfrac{1}{2}\).(\(1-\dfrac{1}{51}\))
=\(\dfrac{1}{2}\).\(\dfrac{50}{51}\)
=\(\dfrac{25}{51}\)
Ta có: \(\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{49\cdot51}\)
\(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{49\cdot51}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{49}-\dfrac{1}{51}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{51}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{50}{51}=\dfrac{25}{51}\)
2x + 6 chia hết cho x + 7
=> 2x + 14 - 8 chia hết cho x + 7
=> 2(x + 7) - 8 chia hết cho x + 7
=> 8 chia hết cho x + 7
=> x + 7 thuộc Ư(8) = {1;2;4;8}
=> x = {-6;-5;-3;1}
=> x = 1
2x+6 chia hết cho x+7
<=> 2x+14)-8 chia hết cho x+7
<=> 2.(x+7) -8 chia hết cho x+7
vì 2.(x+7) chia hết cho x+7 => 8 chia hết cho x+7
=> x+7 thuộc Ư(8)
còn lại tự tìm nha, còn tuy x thuộc Z hay N nữa
\(\dfrac{24}{x+1}=\left(-2\right)^3\)
\(\Leftrightarrow x+1=\dfrac{24}{\left(-2\right)^3}=\dfrac{24}{-8}=-3\)
\(\Rightarrow x=-4\)
13B
14C
b c