chịu thôi

B=64,8

a,

A = 5.(2² . 3² )⁹. (2²)⁶ - 2. (2².3)¹⁴.3⁴ / 5.2²⁸.3¹⁸ - 7.2²⁹.3¹⁸

A = 5.2¹⁸.3¹⁸.2¹² - 2. 2^28. 3¹⁴. 3⁴ / 5. 2²⁸. 3¹⁸ - 7. 2²⁹. 3¹⁸

A = 5.2³⁰.3¹⁸ - 2²⁹. 3¹⁸ /  5.2 ²⁸.3¹⁸ - 7.2²⁹. 3¹⁸

A = 2²⁹. 3¹⁸(5.2-1) / 2²⁸. 3¹⁸ (5 -7.2)

A = 2.9 / -9 = -2

Vậy A = -2

b,

B =81.( 12 - 12/7- 12/289 - 12/85 /  4 - 4/7 - 4/289 - 4/85 :

5 + 5/13 + 5/169 + 5/91 /  6 + 6/13 + 6/169 + 5/91 ) x 158158158

B = 81.[ 12.( 1 - 1/7 - 1/289 - 1/85) / 4.( 1 - 1/7 - 1/289 - 1/85 :

5.(1 + 1/13 + 1/169 + 1/91) / 6.(1+ 1/13 +1/169 + 1/91)] . 2/9

B = 81.[ 3 : 5/6 ] .2/9

B = 81.18/5 . 2/9

B = 1458/5 . 2/9

B = 324/5.

Vậy B = 324/5

CHÚC HỌC TỐT

\(a)\) \(A=\frac{5\left(2^2.3^2\right)^9.\left(2^2\right)^6-2\left(2^2.3\right)^{14}.3^4}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)

\(A=\frac{2^{30}.3^{18}.5-2^{29}.3^{18}}{2^{28}.3^{18}.5-2^{29}.3^{18}.7}\)

\(A=\frac{2^{29}.3^{18}\left(2.5-1\right)}{2^{28}.3^{18}\left(5-2.7\right)}\)

\(A=\frac{2\left(10-1\right)}{5-14}\)

\(A=\frac{2.9}{-9}\)

\(A=-2\)

Vậy \(A=-2\)

\(b)\) \(B=81.\left[\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}\right].\frac{158158158}{711711711}\)

\(B=81.\left[\frac{12\left(1-\frac{1}{7}-\frac{1}{289}-\frac{1}{85}\right)}{4\left(1-\frac{1}{7}-\frac{1}{289}-\frac{1}{85}\right)}:\frac{5\left(1+\frac{1}{13}+\frac{1}{169}+\frac{1}{91}\right)}{6\left(1+\frac{1}{13}+\frac{1}{169}+\frac{1}{91}\right)}\right].\frac{158158158}{711711711}\)

\(B=81.\left[\frac{12}{4}:\frac{5}{6}\right].\frac{2}{9}\)

\(B=81.\frac{18}{5}.\frac{2}{9}\)

\(B=\frac{324}{5}\)

Vậy \(B=\frac{324}{5}\)

Chúc bạn học tốt ~ ( mỏi tay qué >_< ) 

cách này mình tự nghĩ 

\(\hept{\begin{cases}A=\frac{4}{7}+5+\frac{3}{7^2}+\frac{5}{7^3}+\frac{6}{7^4}\\B=\frac{5}{7^4}+5+\frac{6}{7^2}+\frac{4}{7}+\frac{5}{7^3}\end{cases}}\)

\(\Rightarrow A-B=\left(\frac{4}{7}-\frac{4}{7}\right)+\left(\frac{5}{7^3}-\frac{5}{7^3}\right)+\left(5-5\right)+\left(\frac{3}{7^2}-\frac{6}{7^2}\right)+\left(\frac{6}{7^4}-\frac{5}{7^4}\right)\)

\(\Rightarrow A-B=-\frac{3}{7^2}+\frac{1}{7^4}\)

\(\Rightarrow A-B=\frac{-3\times7^2}{7^4}+\frac{1}{7^4}\)

mà \(-3\times7^2< 1\Rightarrow\frac{1}{7^4}>\frac{-3\times7^2}{7^4}\Rightarrow B>A\)

a) $\frac{4}{{25}}:\frac{4}{3} = \frac{4}{{25}} \times \frac{3}{4} = \frac{3}{{25}}$ 

b) $\frac{3}{{14}}:\frac{6}{7} = \frac{3}{{14}} \times \frac{7}{6} = \frac{{3 \times 7}}{{14 \times 6}} = \frac{{3 \times 7}}{{7 \times 2 \times 3 \times 2}} = \frac{1}{4}$

c) $\frac{{12}}{{15}}:2 = \frac{{12}}{{15}} \times \frac{1}{2} = \frac{{12 \times 1}}{{15 \times 2}} = \frac{{6 \times 2 \times 1}}{{15 \times 2}} = \frac{6}{{15}}$           

d) $\frac{{21}}{8}:6 = \frac{{21}}{8} \times \frac{1}{6} = \frac{{21 \times 1}}{{8 \times 6}} = \frac{{7 \times 3 \times 1}}{{8 \times 3 \times 2}} = \frac{7}{{16}}$

Ta có : 

\(S=\frac{3}{2}+\frac{4}{3}+\frac{5}{4}+\frac{6}{5}+\frac{7}{6}+\frac{8}{7}+\frac{9}{8}+\frac{10}{9}+\frac{11}{10}+\frac{12}{11}\)

\(S=\frac{2+1}{2}+\frac{3+1}{3}+\frac{4+1}{4}+...+\frac{11+1}{11}\)

\(S=\left(1+\frac{1}{2}\right)+\left(1+\frac{1}{3}\right)+\left(1+\frac{1}{4}\right)+...+\left(1+\frac{1}{11}\right)\)

\(S=\left(1+1+1+...+1\right)+\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{11}\right)\)

\(S=10+\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{11}\right)>10\) 

\(\Rightarrow\)\(S>10\) 

Vậy \(S>10\)

Chúc bạn học tốt ~ 

Gợi ý: Rút gọn 2 ps, quy đồng rồi so sánh.