`#040911`

\(2^{10}\div8^5\\ =2^{10} \div\left(2^3\right)^5\\=2^{10}\div2^{15}=2^{-5} \)

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\(7^{2x+1}-2.7^4=7^4.5\)

\(\Rightarrow7^{2x+1}=7^4.5+2.7^4\)

\(\Rightarrow7^{2x+1}=7^4.\left(5+2\right)\)

\(\Rightarrow7^{2x+1}=7^4.7\)

\(\Rightarrow7^{2x+1}=7^5\)

\(\Rightarrow2x+1=5\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=2\)

2

= 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/99 - 1/101

= 1/3 - 1/101

= 101/303 - 3/303

= 98/303

2 con 2/ 5x7 và 2/7x5 là sao :/

Gọi d là ƯCLN(4n + 5; 2n + 2)

⇒ (4n + 5) ⋮ d

(2n + 2) ⋮ d ⇒ 2(2n + 2) ⋮ d ⇒ (4n + 4) ⋮ d

⇒ [(4n + 5) - (4n + 4)] ⋮ d

⇒ (4n + 5 - 4n - 4) ⋮ d

⇒ 1 ⋮ d

⇒ d = 1

Vậy 4n + 5 và 2n + 2 là hai số nguyên tố cùng nhau

Gọi ước chung lớn nhất của 4n + 5 và 2n + 2 là: d

Ta có:  4n + 5 ⋮ d

            2n + 2 ⋮ d

       ⇒ 2.(2n+ 2) ⋮ d ⇒ 4n + 4  ⋮ d

        ⇒  4n + 5 - (4n + 4) ⋮ d

             4n + 5  - 4n - 4 ⋮ d 

                                 1 ⋮ d ⇒ d = 1

Ước chung lớn nhất của 4n + 5 và 2n + 2 là 1

Hay 4n + 5 và 2n + 2 là hai số nguyên tố cùng nhau

a) 7/20 + 3/5 + (-1/4)

= 7/20 + 12/20 - 5/20

= 14/20

= 7/10

b) 1/4 + 1/5 + 1/12

= 15/60 + 12/60 + 5/60

= 32/60

= 8/15

c) 1/4 + 1/6 + (-1/12)

= 3/12 + 2/12 - 1/12

= 4/12

= 1/3

d) 3/4 + 7/10 + 11/20

= 15/20 + 14/20 + 11/20

= 40/20 

= 2

a) \(\dfrac{7}{20}\) + \(\dfrac{3}{5}\) + \(\dfrac{-1}{4}\)

= \(\dfrac{7}{20}+\dfrac{12}{20}+\dfrac{-5}{20}\)

= \(\dfrac{14}{20}\)

= \(\dfrac{7}{10}\)

b) \(\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{12}\)

= \(\dfrac{15}{60}+\dfrac{12}{60}+\dfrac{5}{60}\)

= \(\dfrac{32}{60}\)

= \(\dfrac{8}{15}\)

a) x = \(\dfrac{1}{5}+\dfrac{2}{11}\)

    x = \(\dfrac{11}{55}\) + \(\dfrac{10}{55}\)

    x = \(\dfrac{21}{55}\)

b) \(\dfrac{x}{15}\) = \(\dfrac{3}{5}+\dfrac{-2}{3}\)

    \(\dfrac{x}{15}=\dfrac{9}{15}+\dfrac{-10}{15}\)

    \(\dfrac{x}{15}=\dfrac{-1}{15}\)

      \(x=\dfrac{-1}{15}\cdot15\)

       x = -1

c) \(\dfrac{11}{8}+\dfrac{13}{6}=\dfrac{85}{x}\)

    \(\dfrac{33}{24}+\dfrac{52}{24}=\dfrac{85}{x}\)

              \(\dfrac{85}{24}=\dfrac{85}{x}\)

              \(\dfrac{85}{x}=\dfrac{85}{24}\)

               \(x=85:\dfrac{85}{24}\)

               \(x=85\cdot\dfrac{24}{85}\)

               \(x=24\)

a, ( \(\dfrac{1}{4}\) + \(\dfrac{-5}{13}\)) +( \(\dfrac{2}{11}\) + \(\dfrac{-8}{13}\) + \(\dfrac{3}{4}\))

= \(\dfrac{1}{4}\)  - \(\dfrac{5}{13}\) + \(\dfrac{2}{11}\) - \(\dfrac{8}{13}\) + \(\dfrac{3}{4}\)

= ( \(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) - ( \(\dfrac{5}{13}\) + \(\dfrac{8}{13}\)) + \(\dfrac{2}{11}\)

= 1 - 1 + \(\dfrac{2}{11}\)

= \(\dfrac{2}{11}\)

b, ( \(\dfrac{21}{31}\) + \(\dfrac{-16}{7}\)) +( \(\dfrac{44}{53}\) + \(\dfrac{10}{31}\)) + \(\dfrac{9}{53}\)

  =   \(\dfrac{21}{31}-\dfrac{16}{7}+\dfrac{44}{53}+\dfrac{10}{31}+\dfrac{9}{53}\)

    = ( \(\dfrac{21}{31}\) + \(\dfrac{10}{31}\))  + ( \(\dfrac{44}{53}\) + \(\dfrac{9}{53}\))  - \(\dfrac{16}{7}\)

    = 1 + 1 - \(\dfrac{16}{7}\)

     = \(\dfrac{14}{7}-\dfrac{16}{7}\)

     = - \(\dfrac{2}{7}\)

e) \(24=2^3.3\)

\(84=2^2.3.7\)

\(180=2^2.3^2.5\)

\(\RightarrowƯCLN\left(24;84;180\right)=2^2.3=12\)

b) \(24=2^2.3\)

\(36=2^2.3^2\)

\(\RightarrowƯCLN\left(24;36\right)=2^2.3=12\)

g) \(56=2^3.7\)

\(140=2^2.5.7\)

\(\RightarrowƯCLN\left(56;140\right)=2^2.7=28\)

h) \(12=2^2.3\)

\(14=2.7\)

\(8=2^3\)

\(20=2^2.5\)

\(\RightarrowƯCLN\left(12;14;8;20\right)=2\)

d) \(6=2.3\)

\(8=2^3\)

\(18=2.3^2\)

\(\RightarrowƯCLN\left(6;8;18\right)=2\)

k) \(7=7\)

\(9=3^2\)

\(12=2^2.3\)

\(21=3.7\)

\(\RightarrowƯCLN\left(7;9;12;21\right)=1\)

\(1\times\dfrac{4}{9}=\dfrac{4}{9}\)