a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)

\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)

\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)

\(=\dfrac{-1621}{126}\)

b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)

\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)

\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)

\(=-\dfrac{49}{20}\)

\(B=\frac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}\)

\(B=\frac{1+3^4+3^8+3^{12}}{\left(1+3^4+3^8+3^{12}\right)+3^2+3^6+3^{10}+3^{14}}\)

Xét mẫu : \(\left(1+3^4+3^8+3^{12}\right)+3^2\left(1+3^4+3^8+3^{12}\right)=\left(3^2+1\right)\left(1+3^4+3^8+3^{12}\right)\)

Ta có : \(\frac{1+3^4+3^8+3^{12}}{\left(3^2+1\right)\left(1+3^4+3^8+3^{12}\right)}=\frac{1}{3^2+1}=\frac{1}{10}\)

(chủ câu hỏi)

sao lại có \(3^2+1\)ở kia

Tính chất phân phối của phép nhân đối với phép cộng đấy bạn ạ

\(1+3^4+3^8+3^{12}+3^2\left(1+3^4+3^8+3^{12}\right)=1\left(1+3^4+3^8+3^{12}\right)+3^2\left(1+3^4+3^8+3^{12}\right)\)

\(=\left(3^2+1\right)\left(1+3^4+3^8+3^{12}\right)\)như nhau cả thôi bạn

\(\frac{4^{10}+8^4}{4^5+8^6}=\frac{\left(2^2\right)^{10}+\left(2^3\right)^4}{\left(2^2\right)^5+\left(2^3\right)^6}=\frac{2^{2.10}+2^{3.4}}{2^{2.5}+2^{3.6}}=\)

\(=\frac{2^{20}+2^{12}}{2^{10}+2^{18}}\)

\(\frac{4^{10}+8^4}{4^5+8^6}=\frac{2^{20}+2^{12}}{2^{10}+2^{18}}=\frac{2^{12}.2^8+2^{12}}{2^{10}+2^{10}.2^8}=\frac{2^{12}\left(1+2^8\right)}{2^{10}\left(1+2^8\right)}=\frac{2^{12}}{2^{10}}=2^2=4\)

\(A=\dfrac{4^{10}+8^4}{4^5+8^6}\)

\(A=\dfrac{2^{20}+2^{12}}{2^{10}+2^{18}}=\dfrac{\left(2^8+1\right).2^{12}}{\left(1+2^8\right).2^{10}}\)

\(=\dfrac{\left(256+1\right).2^2}{1+256}=\dfrac{257.2^2}{257}=2^2\)

\(B=\dfrac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}\)

\(=\dfrac{1+81+6561+3^{12}}{1+9+81+729+6561+59049+3^{12}+3^{14}}\)

\(=\dfrac{6643+3^{12}}{91+719+6561+59049+3^{12}+3^{14}}\)

\(=\dfrac{6643+3^{12}}{66430+3^{12}+3^{14}}\)

P/s : Nổi hứng lên thì lm chứ k bt đúng hay sai :V

4¹⁰+8⁴ _________

4⁵+8⁶

= 2²⁰+2¹²

________

2¹⁰2⁸+1

=2¹².(2⁸+1) ___________

2¹⁰.(2⁸+1)

=2¹²/2¹⁰=2²=4

= 1/10

\(A=\frac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}\)

Ta có :

\(1+3^4+3^8+3^{12}=\left(3^{16}-1\right):\left(3^4-1\right)\)

\(1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}=\left(3^{16}-1\right):\left(3^2-1\right)\)

\(\Rightarrow A=\frac{\left(3^{16}-1\right):\left(3^4-1\right)}{\left(3^{16}-1\right):\left(3^2-1\right)}=\frac{3^2-1}{3^4-1}=\frac{1}{10}\)

=\(\frac{1}{10}\) 

Violympic ak,mk làm òi

Ta có

•   A=1+3⁴+3⁸+3¹²

=>3⁴.A=3⁴+3⁸+3¹²+3¹⁶

<=>81.A-A=3¹⁶-1

<=>A=(3¹⁶-1)/80=538084

•B=1+3²+3⁴+3⁶+3⁸+3¹⁰+3¹²+3¹⁴

=>3².B=3²+3⁴+3⁶+3⁸+3¹⁰+3¹²+3¹⁴+3¹⁶

<=>8.B=3¹⁶-1

<=>B=(3¹⁶-1)/8=53808400

Vậy Q=A/B=538084/53808400=1/100=0.01

Sửa lại:

B=5380840

=>Q=1/10

\(Q=\frac{1+3^4+3^8+3^{12}}{\left(1+3^4+3^8+3^{12}\right)+3^2\left(1+3^4+3^8+3^{12}\right)}\)

\(Q=\frac{1+3^4+3^8+3^{12}}{10\left(1+3^4+3^8+3^{12}\right)}=\frac{1}{10}\)

Cj ko rep đc kịp sr nha