\(\dfrac{6^6+2^7.3^6+2^6.3^7}{4.2^3.3^2.2^2}\)

\(=\dfrac{\left(2^2.3\right)^6+2^7.3^6+2^6.3^7}{2^2.2^3.3^2.2^2}\)\(=\dfrac{2^{12}.3^6+2^7.3^6+2^6.3^7}{2^7.3^2}\)

\(=\dfrac{2^6.3^6.\left(2^6+2+3\right)}{2^7.3^2}\)\(=\dfrac{3^4.69}{2}=\dfrac{5589}{2}\)

`@` `\text {Ans}`

`\downarrow`

\(\dfrac{2^8-2^3}{2^5-1}=\dfrac{2^3\left(2^5-1\right)}{2^5-1}=\dfrac{2^3}{1}=2^3=8\)

_____

\(\dfrac{4^8\cdot9^4}{6^6\cdot8^3}\)

`=`\(\dfrac{\left(2^2\right)^8\cdot\left(3^2\right)^4}{2^6\cdot3^6\cdot\left(2^3\right)^3}\)

`=`\(\dfrac{2^{16}\cdot3^8}{2^6\cdot3^6\cdot2^9}\)

`=`\(\dfrac{2^{16}\cdot3^8}{2^{15}\cdot3^6}\)

`=`\(\dfrac{3^2}{2}\) `=`\(\dfrac{9}{2}\)

______

\(\dfrac{27^4\cdot2^3-3^{10}\cdot4^3}{6^4\cdot9^3}\)

`=`\(\dfrac{\left(3^3\right)^4\cdot2^3-3^{10}\cdot\left(2^2\right)^3}{2^4\cdot3^4\cdot\left(3^2\right)^3}\)

`=`\(\dfrac{3^{12}\cdot2^3-3^{10}\cdot2^6}{2^4\cdot3^4\cdot3^6}\)

`=`\(\dfrac{3^{10}\cdot\left(3^2\cdot2^3-2^6\right)}{3^{10}\cdot2^4}\)

`=`\(\dfrac{72-2^6}{2^4}=\dfrac{8}{16}=\dfrac{1}{2}\)

\(\dfrac{2^8-2^3}{2^5-1}=\dfrac{2^3\left(2^5-1\right)}{2^5-1}=2^3=8\)

\(\dfrac{4^8.9^4}{6^6.8^3}=\dfrac{2^{16}.3^8}{2^6.3^6.2^9}=2.3^2=18\)

\(\dfrac{27^4.2^3-3^{10}.4^3}{6^4.9^3}=\dfrac{3^{12}.2^3-3^{10}.2^6}{2^4.3^4.3^6}=\dfrac{2^3.3^{10}.\left(3^2-2^3\right)}{2^4.3^{10}}=\dfrac{9-8}{2}=\dfrac{1}{2}\)

a) \(\left(-\dfrac{2}{3}+\dfrac{3}{7}\right):\dfrac{4}{5}+\left(-\dfrac{1}{3}+\dfrac{4}{7}\right):\dfrac{4}{5}\)

\(=\left(-\dfrac{5}{21}\right):\dfrac{4}{5}+\left(\dfrac{5}{21}\right):\dfrac{4}{5}\)

\(=\left(-\dfrac{5}{21}+\dfrac{5}{21}\right):\dfrac{4}{5}\)

\(=0:\dfrac{4}{5}\)

\(=0\)

b) \(\dfrac{5}{9}:\left(\dfrac{1}{11}-\dfrac{5}{22}\right)+\dfrac{5}{9}:\left(\dfrac{1}{15}-\dfrac{2}{3}\right)\)

\(=\dfrac{5}{9}:\left(-\dfrac{3}{22}\right)+\dfrac{5}{9}:\left(-\dfrac{3}{5}\right)\)

\(=\dfrac{5}{9}:\left[\left(-\dfrac{3}{22}\right)+\left(-\dfrac{3}{5}\right)\right]\)

\(=\dfrac{5}{9}:\left(-\dfrac{81}{110}\right)\)

\(=-\dfrac{550}{729}\)

c) \(4^2.4^3:4^{10}\)

\(=\dfrac{4^5}{4^{10}}\)

\(=\dfrac{1}{4^5}\)

\(=\dfrac{1}{256}\)

d) \(\left(0,6\right)^5:\left(0,2\right)^6\)

\(=\dfrac{\left(0,2\cdot3\right)^5}{\left(0,2\right)^6}\)

\(=\dfrac{\left(0,2\right)^5\cdot3^5}{\left(0,2\right)^6}\)

\(=\dfrac{243}{0,2}\)

\(=1215\)

Mai mốt bạn đăng một lần ít thôi nha tại giờ khuya quá nên mình chỉ làm đến đây thôi =))

Bài làm:

Bài 1

a) \(\left(x-\frac{1}{2}\right)^2=0\) 

 \(\rightarrow\left(x-\frac{1}{2}\right)^2=0^2\)

 \(\rightarrow x-\frac{1}{2}=0\) 

 \(\Rightarrow x=\frac{1}{2}\)

Bài 2

a) \(25^3\div5^2=\left(5^2\right)^3\div5^2=5^6\div5^2=5^4\)

b) \(\left(\frac{3}{7}\right)^{21}\div\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}\div\left[\left(\frac{3}{7}\right)^2\right]^6=\left(\frac{3}{7}\right)^{21}\div\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^9\)

c) \(3-\left(\frac{-6}{7}\right)^0+\left(\frac{1}{2}\right)^2\div2=3-1+\frac{1}{4}\times\frac{1}{2}=2+\frac{1}{8}=\frac{17}{8}\)

Bài 3

a) \(9\times3^3\times\frac{1}{81}\times3^2=3^2\times3^3\times\frac{1}{3^4}\times3^2=3^3\)

b) \(4\times2^5\div\left(2^3\times\frac{1}{16}\right)=2^2\times2^5\div\left(2^3\times\frac{1}{2^4}\right)=2^7\div\frac{1}{2}=2^6\)

c) \(3^2\times2^5\times\left(\frac{2}{3}\right)^2=3^2\times2^5\times\frac{2^2}{3^2}=3^2\times\frac{2^7}{3^2}=2^7\)

d) \(\left(\frac{1}{3}\right)^2\times\frac{1}{3}\times9^2=\left(\frac{1}{3}\right)^3\times3^4=\frac{1}{3^3}\times3^4=3^1\)

Các bạn giải từng bước ra cho mình nhé, cảm ơn các bạn

các bạn ko phải làm bài 3 nữa nhé

\(\dfrac{9^4\cdot2-3^6}{34\cdot37}=\dfrac{3^8\cdot2-3^6}{34\cdot37}=\dfrac{3^6\cdot\left(18-1\right)}{34\cdot37}=\dfrac{3^6}{2\cdot37}=\dfrac{729}{74}\)

4: =>3x=-6

hay x=-2

a) (1/3)⁵⁰ . (-9)²⁵ .2/3:4

= (1/3)⁵⁰ . [-(3)⁵⁰] . 2/3 . 1/4

= - (1/3.3)⁵⁰ . 1/6

= -1 . 1/6 = -1/6

b) (2⁴.2⁶)/(2⁵)² - (2⁵.15³)/(6³.10²)

= 2¹⁰/2¹⁰ - (2⁵.3³.5³)/(2³.3³.2².5²)

= 1- (2⁵.3³.5³)/(2⁵.3³.5²)

= 1- 5

= -4

\(=\frac{2^{10}}{2^{10}}-\frac{2^5.3^3.5^3}{2^3.3^3.2^2.5^2}\)

\(=1-5=-4\)

ik nhé. tks bạn!