\(\begin{array}{l}{\left( {\frac{{ - 2}}{3}} \right)^3} = \frac{{{{\left( { - 2} \right)}^3}}}{{{3^3}}} = \frac{{ - 8}}{{27}};\\{\left( {\frac{{ - 3}}{5}} \right)^2} = \frac{{{{\left( { - 3} \right)}^2}}}{{{5^2}}} = \frac{9}{{25}};\\{\left( { - 0,5} \right)^3} = {\left( {\frac{{ - 1}}{2}} \right)^3} = \frac{{{{\left( { - 1} \right)}^3}}}{{{2^3}}} = \frac{{ - 1}}{8};\\{\left( { - 0,5} \right)^2}=\frac{{{{\left( { - 1} \right)}^2}}}{{{2^2}}} = \frac{{1}}{4};\\\,{\left( {37,57} \right)^0} = 1;\,\\{\left( {3,57} \right)^1} = 3,57.\end{array}\)

\(\left|0,5-x\right|=\left|-0,5\right|\)

\(\left|0,5-x\right|=0,5\)

\(\Leftrightarrow\left[{}\begin{matrix}0,5-x=0,5\\0,5-x=-0,5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0,5-0,5\\x=\left(-0,5\right)-0,5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)

Chúc bạn học tốt!

a: =>|x-1/4|=3/4

=>x-1/4=3/4 hoặc x-1/4=-3/4

=>x=1 hoặc x=-1/2

b: \(\left|x+\dfrac{1}{2}\right|=\dfrac{1}{2}-\dfrac{9}{4}=\dfrac{2-9}{4}=-\dfrac{7}{4}\)(vô lý)

c: \(\Leftrightarrow\left[{}\begin{matrix}2x+5=1-x\\2x+5=x-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=-4\\x=-6\end{matrix}\right.\Leftrightarrow x\in\left\{-\dfrac{4}{3};-6\right\}\)

e: =>|3/2-x|=0

=>3/2-x=0

hay x=3/2

\(a,0,1^{2-x}>0,1^{4+2x}\\ \Leftrightarrow2-x>2x+4\\ \Leftrightarrow3x< -2\\ \Leftrightarrow x< -\dfrac{2}{3}\)

\(b,2\cdot5^{2x+1}\le3\\ \Leftrightarrow5^{2x+1}\le\dfrac{3}{2}\\ \Leftrightarrow2x+1\le log_5\left(\dfrac{3}{2}\right)\\ \Leftrightarrow2x\le log_5\left(\dfrac{3}{2}\right)-1\\ \Leftrightarrow x\le\dfrac{1}{2}log_5\left(\dfrac{3}{2}\right)-\dfrac{1}{2}\\ \Leftrightarrow x\le log_5\left(\dfrac{\sqrt{30}}{10}\right)\)

c, ĐK: \(x>-7\)

\(log_3\left(x+7\right)\ge-1\\ \Leftrightarrow x+7\ge\dfrac{1}{3}\\ \Leftrightarrow x\ge-\dfrac{20}{3}\)

Kết hợp với ĐKXĐ, ta có:\(x\ge-\dfrac{20}{3}\)

d, ĐK: \(x>\dfrac{1}{2}\)

\(log_{0,5}\left(x+7\right)\ge log_{0,5}\left(2x-1\right)\\ \Leftrightarrow x+7\le2x-1\\ \Leftrightarrow x\ge8\)

Kết hợp với ĐKXĐ, ta được: \(x\ge8\)

a) \(\left[\left(-2,7\right)^4\right]^5-\left[\left(-2,7\right)^2\right]^{20}\)

\(=\left(-2,7\right)^{20}-\left(-2,7\right)^{20}\)

\(=0\)

b) \(\left(-0,5\right)^5:\left(-0,5\right)^3-\left(\dfrac{17}{2}\right)^7:\left(\dfrac{17}{2}\right)^6\)

\(=\left(-0,5\right)^2-\dfrac{17}{2}\)

\(=0,25-\dfrac{17}{2}\)

\(=-8,25\)

c) \(\left(8^{14}:4^{12}\right):\left(16^6:8^2\right)\)

\(=8^{14}:4^{12}:16^6\cdot8^2\)

\(=2^{48}:2^{24}:2^{24}\)

\(=0\)

Cái cuối bằng 1 nhé!

Sửa lại cái cuối cùng đáp án bằng 0 thôi, còn cách giải chi tiết mình làm đúng rồi nhé. Bởi:

\(2^{48}:2^{24}:2^{24}=2^0=1\)

\(=\frac{\left(0,5\right)^5.2^9}{2^6.2^4}=\frac{\left(0,5\right)^5.2^9}{2^9.2}=\left(\frac{1}{2}\right)^5\div2\)

\(=\frac{1^5}{2^5}.\frac{1}{2}=\frac{1}{2^6}=\frac{1}{64}\)

=\(\frac{16}{1024}\)=\(\frac{1}{64}\)

Lời giải:

$3(|x|-\frac{4}{5})+0,2=0,5$

$3(|x|-\frac{4}{5})=0,3$

$|x|-\frac{4}{5}=0,3:3=0,1$

$|x|=0,1+\frac{4}{5}=0,9$

$\Rightarrow x=\pm 0,9$

\(\frac{2^3.\left(0,5\right)^3.3^7}{2.\left(0,5\right)^4.3^8}=\frac{2^3.\left(\frac{1}{2}\right)^3.3^7}{2.\left(\frac{1}{2}\right)^4.3^8}=\frac{2^3.\frac{1^3}{2^3}.3^7}{2.\frac{1^4}{2^4}.3^8}=\frac{1.3^7}{\frac{1}{2^3}.3^8}=\frac{3^7}{\frac{3^8}{2^3}}=3^7.\frac{2^3}{3^8}=\frac{2^3}{3}=\frac{8}{3}\)

(9^5.5^7)/(45^7)

Hình vẽ:

Tứ giác GHIK là hình vuông.

Hình vẽ:

Tứ giác GHIK là hình vuông.