Tham khảo:

a)      \((4{x^2} - 5):(x - 2) = \dfrac{{4{x^2} - 5}}{{x - 2}} = 4x + 8 + \dfrac{{11}}{{x - 2}}\)

Vậy \( (4{x^2} - 5):(x - 2)= 4x + 8 + \dfrac{{11}}{{x - 2}}\)

b)      \((3{x^3} - 7x + 2):(2{x^2} - 3) = \dfrac{{3{x^3} - 7x + 2}}{{2{x^2} - 3}}\)

Vậy \( (3{x^3} - 7x + 2):(2{x^2} - 3)= \dfrac{3}{2}x + \dfrac{{\dfrac{-5}{2}x + 2}}{{2{x^2} - 3}}\)

\(a)(2{y^4} - 13{y^3} + 15{y^2} + 11y - 3):({y^2} - 4y - 3)=2y^2-5y+1\)

b) \((5{x^3} - 3{x^2} + 10):({x^2} + 1)=5x-3+\dfrac{-5x+13}{x^2+1}\)

Tham khảo:

a) \((8{x^6} - 4{x^5} + 12{x^4} - 20{x^3}):4{x^3}\)

\( = (8{x^6}:4{x^3}) - (4{x^5}:4{x^3}) + (12{x^4}:4{x^3}) - (20{x^3}:4{x^3})\)

\( = 2{x^2} - {x^2} + 3x - 5\)

b) 

Vậy \((2{x^2} - 5x + 3):(2x - 3)= x - 1\)

\(\begin{array}{l}a)\frac{{4{\rm{x}} - 6}}{{5{{\rm{x}}^2} - x}}.\frac{{25{{\rm{x}}^2} - 10{\rm{x}} + 1}}{{27 + 8{{\rm{x}}^3}}}\\ = \frac{{ - 2\left( {3 - 2{\rm{x}}} \right)}}{{x\left( {5{\rm{x}} - 1} \right)}}.\frac{{{{\left( {5{\rm{x}} - 1} \right)}^2}}}{{\left( {3 - 2{\rm{x}}} \right)\left( {9 + 6{\rm{x}} + 4{{\rm{x}}^2}} \right)}}\\ = \frac{{ - 2\left( {5{\rm{x}} - 1} \right)}}{{x\left( {9 + 6{\rm{x}} + 4{{\rm{x}}^2}} \right)}}\\b)\frac{{2{\rm{x}} + 10}}{{{{\left( {x - 3} \right)}^2}}}:\frac{{{{\left( {x + 5} \right)}^3}}}{{{x^2} - 9}}\\ = \frac{{2{\rm{x}} + 10}}{{{{\left( {x - 3} \right)}^2}}}.\frac{{{x^2} - 9}}{{{{\left( {x + 5} \right)}^2}}}\\ = \frac{{2\left( {x + 5} \right)\left( {x - 3} \right)\left( {x + 3} \right)}}{{{{\left( {x - 3} \right)}^2}{{\left( {x + 5} \right)}^3}}}\\ = \frac{{2\left( {x + 3} \right)}}{{\left( {x - 3} \right){{\left( {x + 5} \right)}^2}}}\end{array}\)

\(a.\dfrac{3^{27}}{9^6.3^{16}}=\dfrac{3^{27}}{3^{12}.3^{16}}=\dfrac{3^{27}}{3^{28}}=\dfrac{1}{3}\)

\(\left(x-\dfrac{5}{2}\right)^2=\dfrac{9}{4}\\ \Rightarrow x-\dfrac{5}{2}=\pm\dfrac{3}{2}\)

\(TH1:x-\dfrac{5}{2}=\dfrac{3}{2}\Rightarrow x=\dfrac{3}{2}+\dfrac{5}{2}=\dfrac{8}{2}=4\)

\(TH2:x-\dfrac{5}{2}=-\dfrac{3}{2}\Rightarrow x=-\dfrac{3}{2}+\dfrac{5}{2}=\dfrac{2}{2}=1\)

a: \(=\dfrac{3^{27}}{3^{12}\cdot3^{16}}=\dfrac{1}{3}\)

Bài 1: Thực hiện phép tính:

a) 5⁰ . 79 + 24 : 2³ - 15

= 1 . 79 + 24 : 8 - 15

= 79 + 3 - 15

= 82 - 15

= 67.

b) 27 . 34 + 34 . 73

= (27 + 73) . 34

= 100 . 34

= 3400.

c) 4³ . 46 + 54 . 4³ - 120

= 4³. (46 + 54) - 120

= 64 . 100 - 120

= 6400 - 120

= 6280.

d) 2 + 3 + 4 + ... + 69 + 70

= (70 + 2) . [(70 - 2) : 1 + 1] : 2

= 72 . 69 : 2

= 4968 : 2

= 2484.

Bài 2: Tìm số tự nhiên x, biết:

a) 5^x = 25

\(\Rightarrow\) 5^x = 5²

\(\Rightarrow\) x = 2.

b) 3^{x + 2} = 81

3^x . 3² = 81

\(\Rightarrow\) 3^x . 3² = 3⁴

\(\Rightarrow\) x + 2 = 4

x = 4 - 2

x = 2.

c) (x + 1)³ = 27

\(\Rightarrow\) (x + 1)³ = 3³

\(\Rightarrow\) x + 1 = 3

x = 3 - 1

x = 2.

d) 6 : (2x - 1) + 45 = 49⁰ . 47

6 : (2x - 1) + 45 = 1 . 47

6 : (2x - 1) + 45 = 47

6 : (2x - 1) = 47 - 45

6 : (2x - 1) = 2

2x - 1 = 6 : 2

2x - 1 = 3

2x = 3 + 1

2x = 4

x = 4 : 2

x = 2.

Bài 3: Tính:

a) 27 . 75 + 25 . 27 - 100

= 27 . (75 + 25) - 100

= 27 . 100 - 100

= 2700 - 100

= 2600.

b) 4⁷ : 4⁵ - 35 : 5 + 27 : 3²

= 4² - 7 + 27 : 9

= 16 - 7 + 3

= 9 + 3

= 12.

c) 2¹⁰ : 2⁷ + 4003⁰ . 29 - 135 : 45

= 2³ + 1 . 29 - 135 : 45

= 8 + 29 - 3

= 37 - 3

= 34.

d) 12 : {390 : [500 - (125 + 35 . 7)]}

= 12 : {390 : [500 - (125 + 245)]

= 12 : {390 : [500 - 370]}

= 12 : {390 : 130}

= 12 : 3

= 4.

nhiều thế

Giải:

Bài 1:

\(707-3\left(x+3\right)=407\)

\(\Leftrightarrow3\left(x-3\right)=300\)

\(\Leftrightarrow x+3=100\)

\(\Leftrightarrow x=97\)

Vậy \(x=97\).

Bài 2:

a) \(143-43.\left[\left(25:5\right)^2-5^2\right]\)

\(=143-43.\left(5^2-5^2\right)\)

\(=143-43.1\)

\(=143-43=100\)

b) \(7:7+49\left(2^3.15-5.4\right)\)

\(=1+49.\left(120-20\right)\)

\(=1+49.100\)

\(=4901\)

c) \(\left(2^3.9^4+9^3.45\right):\left(9^2.10-9^2\right)\)

\(=\left(8.9^4+9^4.5\right):\left(9^2.10-9^2\right)\)

\(=\left[9^4\left(8+5\right)\right]:\left[9^2\left(10-1\right)\right]\)

\(=9^4.13:9^3\)

\(=9.13=117\)

Chúc bạn học tốt!

Bạn ơi, bạn viết lại đề đi. Khó nhìn quá

a: =16-2+91=14+91=105

b: =9*5+8*10-27=45+53=98

c: =32+65-3*8=8+65=73

d; \(=5^3-10^2=125-100=25\)

e: \(=4^2-3^2+1=8\)

f: =9*16-16*8-8+16*4

=16(9-8+4)-8

=16*5-8

=72

a) \(2^4-50:25+13\cdot7\)

\(=2^4-2+91\)

\(=16-2+91\)

\(=14+91\)

\(=105\)

b) \(3^2\cdot5+2^3\cdot10-3^4:3\)

\(=9\cdot5+8\cdot10-3^3\)

\(=45+80-27\)

\(=98\)

c) \(2^5+5\cdot13-3\cdot2^3\)

\(=32+65-3\cdot8\)

\(=32+65-24\)

\(=73\)

d) \(5^{13}:5^{10}-5^2\cdot2^2\)

\(=5^{13-10}-\left(5\cdot2\right)^2\)

\(=5^3-10^2\)

\(=125-100\)

\(=25\)

e) \(4^5:4^3-3^9:3^7+5^0\)

\(=4^{5-3}-3^{9-7}+1\)

\(=4^2-3^2+1\)

\(=16-9+1\)

\(=8\)

f) \(3^2\cdot2^4-2^3\cdot4^2-2^3\cdot5^0+4^2\cdot2^2\)

\(=3^2\cdot4^2-2^3\cdot4^2-2^3\cdot1+4^2\cdot2^2\)

\(=4^2\cdot\left(3^2-2^3+2^2\right)-2^3\)

\(=4^2\cdot\left(9-8+4\right)-8\)

\(=16\cdot5-8\)

\(=72\)