\(N=\dfrac{3^{10}.11+3^9.15}{3^9.2^4}=\dfrac{3^9.33+3^9.15}{3^9.2^4}\)

\(=\dfrac{3^9\left(33+15\right)}{3^9.16}\)

\(=\dfrac{48}{16}=3\)

\(A=\dfrac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}=\dfrac{3^{10}\cdot\left(11+5\right)}{3^9\cdot16}=\dfrac{3^{10}\cdot16}{3^9\cdot16}=3\)

\(B=\dfrac{2^{10}\cdot13+2^{10}\cdot65}{2^8\cdot104}=\dfrac{2^{10}\cdot\left(13+65\right)}{2^8\cdot2^2\cdot26}=\dfrac{2^{10}\cdot78}{2^{10}\cdot26}=3\)

\(C=\dfrac{72^3\cdot54^2}{108^4}=\dfrac{\left(2^3\cdot3^2\right)^3\cdot\left(2\cdot3^3\right)^2}{\left(3^3\cdot2^2\right)^4}\\ =\dfrac{2^9\cdot3^6\cdot2^4\cdot3^6}{3^{12}\cdot2^8}=\dfrac{2^{13}\cdot3^{12}}{3^{12}\cdot2^8}=2^5=32\)

\(D=\dfrac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}=\dfrac{11\cdot3^{29}-\left(3^2\right)^{15}}{2^2\cdot3^{28}}=\dfrac{11\cdot3^{29}-3^{30}}{2^2\cdot3^{28}}\\ =\dfrac{3^{29}\cdot\left(11-3\right)}{2^2\cdot3^{28}}=\dfrac{3^{29}\cdot8}{4\cdot3^{28}}=3\cdot2=6\)

Lời giải:
a.

\(\frac{n+1}{n+2}=\frac{n+1}{n+2}+1-1=\frac{2n+3}{n+2}-1\)

\(> \frac{2n+3}{n+3}-1=\frac{(n+3)+n}{n+3}-1=\frac{n}{n+3}\)

b.

\(10A=\frac{10^{12}-10}{10^{12}-1}=\frac{(10^{12}-1)-9}{10^{12}-1}=1-\frac{9}{10^{12}-1}<1\)

\(10B=\frac{10^{11}+10}{10^{11}+1}=\frac{(10^{11}+1)+9}{10^{11}+1}=1+\frac{9}{10^{11}+1}>1\)

$\Rightarrow 10A< 10B\Rightarrow A< B$

Q=(2^9.3+2^9.5):2^12

Đặt A=2^9.3+2^9.5

      A=2^9.(3+5)

      A=2^9.8

Mặt khác:8=2^3

=>A=2^9.2^3

     A=2^12

Theo đề bài ta có Q=(2^9.3+2^9.5):2^12

=>Q=2^12:2^12

    Q=1

Nhìn dài dòng thế thôi chứ đơn giản lắm.Nếu thấy đúng thì cho mình nhé!

\(\frac{3^{10}.11+3^{10}.5}{3^9.2^4}+\frac{2^{13}+2^5}{2^{10}+2^2}=11\)

-x + 20 = - (-15) - (8) + 13 

-x + 20 = 15 - 8 + 13 

-x + 20 = 7 + 13 

- x + 20 = 20

x = 20 - 20 

x = 0

-(-10) + x = -13 + (-9) + (-6) 

10 + x = -13 - 9 - 6 

10 + x = -28 

x = -28 - 10 

x = -38 

N=1/2+1/2²+...+1/2¹⁰

2N=1+1/2+...+1/2⁹

2N-N=1-1/2¹⁰=1-1/1024=1023/1024

Giải:

N=1/2+1/2²+1/2³+...+1/2⁹+1/2¹⁰

2N=1+1/2+1/2²+...+1/2⁸+1/2⁹

2N-N=(1+1/2+1/2²+...+1/2⁸+1/2⁹)-(1/2+1/2²+1/2³+...+1/2⁹+1/2¹⁰)

N=1-1/2¹⁰=1023/1024

Chúc bạn học tốt!

a)\(A=\frac{3^{10}.11+3^{10}.5}{3^9.2^4}=\frac{3^{10}\left(11+5\right)}{3^9.2^4}=\frac{3.16}{2^4}=\frac{3.2^4}{2^4}=3\)

b)\(B=\frac{2^{10}.13+2^{10}.65}{2^8.104}=\frac{2^{10}\left(13+65\right)}{2^8.2^3.13}=\frac{2^{10}.78}{2^{11}.13}=3\)

c)\(C=\frac{4^9.36+64^4}{16^4.100}=\frac{2^{18}.2^2.3^2+2^{24}}{2^{16}.2^2.5^2}=\frac{2^{20}\left(3^2+2^4\right)}{2^{18}.5^2}=\frac{2^2.25}{25}=4\)