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a) \(\dfrac{790^4}{79^4}\) = \(\dfrac{79^4.10^4}{79^4}\) = 10⁴ = 10000

b) \(\dfrac{3^2}{0,375^2}\) = \(\dfrac{0,375^2.8^2}{0,375^2}\) = 8² = 64

c) \(3^2.\dfrac{1}{243}.81^2.\dfrac{1}{3^3}\) = 3² . 3^-5 . 3⁸ . 3^-3 = 3² = 9

d) \(\left(4.2^5\right):\left(2^3.\dfrac{1}{16}\right)\) = 2⁷ : (2³ . 2^-4) = 2⁷ : 2^-1 = 2⁷ : 1/2 = 2⁸

\(a;3^2\cdot\frac{1}{243}\cdot81^2\cdot\frac{1}{3^3}\)

\(=3^2\cdot\frac{1}{3^5}\cdot3^4\cdot\frac{1}{3^3}\)

\(=\left(3^2\cdot3^4\right)\cdot\left(\frac{1}{3^5}\cdot\frac{1}{3^3}\right)\)

\(=3^6\cdot\frac{1}{3^8}\)

\(=\frac{3^6}{3^8}\)

\(=\frac{1}{3^2}=\frac{1}{9}\)

\(3^2.\frac{1}{243}.81^2.\frac{1}{3^3}\)

= \(9.\frac{1}{243}.6561.\frac{1}{27}\)

= \(9\)

b ) \(\left(4,2\right)^5:\left(2^3.\frac{1}{16}\right)\)

= \(\left(\frac{21}{5}\right)^5:\left(8.\frac{1}{16}\right)\)

= \(130691232:\frac{1}{2}\)

= \(130691232\times2\)

= 261382464

Chúc bạn học tốt  !!!

= 

1.a, \(3^2.\frac{1}{243}.81^2.\frac{1}{3^3}=\frac{3^2}{3^5}.\frac{\left(3^4\right)^2}{3^3}\)\(=\frac{3^2.3^8}{3^5.3^3}=\frac{3^{10}}{3^8}=3^2=9\)\(\)

b,  \(\left(4.2\right)^5:\left(2^3.\frac{1}{16}\right)=8^5:\left(8.\frac{1}{16}\right)\)\(=8^5:\frac{1}{2}=\left(2^3\right)^5.2=2^{15}.2=2^{16}\)

chúc bn học tốt!

Câu một \(=3^2.\frac{1}{3^5}.\left(3^4\right)^2.\frac{1}{3^3}=3^{10}.\frac{1}{3^8}=3^2=9\)

Câu hai \(=\left(2^2.2^5\right):\left(2^3.\frac{1}{2^4}\right)=\frac{2^7}{\frac{2^3}{2^4}}=2^8=256\)

Chờ chút nhá :D

Câu 3  \(=9-64-25^2=-680\)

Câu 4 \(=8+1-1+1=9\)

Câu 5 \(=4,75-0,37+0,125-1,28-2,5+3\frac{1}{12}=0,725+3\frac{1}{12}=3\frac{97}{120}\)

Sai thì mình xin lỗi :v, vội quá

Câu 1:\(3^2.\frac{1}{243}.81^2.\frac{1}{3^3}=3^2.\frac{1}{3^5}.3^8.\frac{1}{3^3}=3^2:3^5.3^8:3^3=3^{2-5+8-3}=3^2=9\)

a) = \(\frac{7}{2}\)

b) = \(\frac{643}{64}\)

c) = 0

a) \(A=\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{2019}}\)

\(5A=\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{2018}}\)

\(4A=5A-A=\frac{1}{5}-\frac{1}{5^{2019}}\)

\(A=\frac{1}{20}-\frac{1}{4.5^{2019}}< \frac{1}{20}< \frac{1}{2}\)

b)  Đề có sai không mà đằng cuối lại là \(\frac{1}{4^2}\)lặp lại lần nữa.
c) \(C=\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}\)

\(2C=1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}-\frac{1}{32}\)

\(3C=2C+C=1-\frac{1}{64}< 1\)

\(C< \frac{1}{3}\)

d) Xem lại đề nữa đi e, nếu trừ hai vế cho \(\frac{1}{3}\)thì vế trái > 0 > vế phải rồi
e)  \(\frac{1}{41}+\frac{1}{42}+...+\frac{1}{50}>\frac{1}{50}+\frac{1}{50}+...+\frac{1}{50}\)(10 số hạng)
                                                    \(=\frac{10}{50}=\frac{1}{5}\)

Tương tự: \(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{60}>\frac{1}{6}\)

\(\frac{1}{61}+\frac{1}{62}+...+\frac{1}{70}>\frac{1}{7}\)

\(\frac{1}{71}+\frac{1}{72}+...+\frac{1}{80}>\frac{1}{8}\)

\(\frac{1}{41}+\frac{1}{42}+...+\frac{1}{80}>\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}=\frac{533}{840}>\frac{490}{840}=\frac{7}{12}\)

a: \(\dfrac{1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}}{1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}}:\dfrac{13+\dfrac{13}{2}+\dfrac{13}{3}+\dfrac{13}{4}}{17-\dfrac{17}{2}+\dfrac{17}{3}-\dfrac{17}{4}}\)

\(=\dfrac{1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}}{1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}}\cdot\dfrac{17\left(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}\right)}{13\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}\right)}=\dfrac{17}{13}\)

b: \(\dfrac{0.125-\dfrac{1}{5}+\dfrac{1}{7}}{0.375-\dfrac{3}{5}+\dfrac{3}{7}}+\dfrac{\dfrac{1}{2}+\dfrac{1}{3}-0.2}{\dfrac{3}{4}+0.5-\dfrac{3}{10}}\)

\(=\dfrac{\dfrac{1}{8}-\dfrac{1}{5}+\dfrac{1}{7}}{\dfrac{3}{8}-\dfrac{3}{5}+\dfrac{3}{7}}+\dfrac{\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{5}}{\dfrac{3}{4}+\dfrac{3}{6}-\dfrac{3}{10}}\)

\(=\dfrac{1}{3}+\dfrac{\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{5}}{\dfrac{3}{2}\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{5}\right)}=\dfrac{1}{3}+\dfrac{2}{3}=1\)

A, \(\frac{81}{11}\)

B,\(256\)

Câu C sai

(2/5+2/7-2/11):(3/7-3/11+3/5) =2/5+2/7-2/11.7/3-11/3+5/3=2/1+2/1-2/1.1/3-1/3+1/3=2+1/3=7/3                                                                          Em đây mới học lớp 6 nên hay xem kĩ lại và tính bang máy tính  

a, 2/3

b,1

nhớ nhé