\(4.8^6.2.8^3=4.2.8^{6+3}=4.2.8^9=8.8^9=8^{9+1}=8^{10}\)

a, đk : \(x\ne3\\ \)

\(\dfrac{x-2}{x-3}>0\\ \Leftrightarrow x-2>\\\Leftrightarrow x>2\)

Vậy \(x>2;x\ne3\)

b, đk : \(x\ne-\dfrac{1}{2}\)\

\(\dfrac{4x+3}{2x+1}< 2\\ \Leftrightarrow\dfrac{4x+3}{2x+1}-2< 0\\ \Leftrightarrow\dfrac{4x+3-2\left(2x+1\right)}{2x+1}< 0\\ \Leftrightarrow\dfrac{4x+3-4x-2}{2x+1}< 0\\ \Leftrightarrow\dfrac{1}{2x+1}< 0\)

vì \(1>0\)

\(\Rightarrow2x+1< 0\\ \Leftrightarrow x< -\dfrac{1}{2}\)

Vậy \(x< -\dfrac{1}{2}\)

\(A=-5x^3y-14xy^2-9-12x^2y\)

Thay \(x=-1;y=-\dfrac{1}{2}\) vào A

\(A=-5.\left(-1\right)^3.\left(-\dfrac{1}{2}\right)-14.\left(-1\right).\left(-\dfrac{1}{2}\right)^2-9-12.\left(-1\right)^2.\left(-\dfrac{1}{2}\right)=-2\)

Vậy với \(x=-1;y=-\dfrac{1}{2}\) thì A \(=-2\)

\(2^n.16-2^{n+1}=2^6-2^3\\ \Leftrightarrow2^n.2^4-2^n.2=2^6-2^3\\ \Leftrightarrow2^n\left(2^4-2\right)=2^6-2^3\\ \Leftrightarrow2^n=\dfrac{2^6-2^3}{2^4-2}\\ \Leftrightarrow2^n=\dfrac{2\left(2^5-2^2\right)}{2\left(2^3-1\right)}\\ \Leftrightarrow2^n=\dfrac{28}{6}\\ \Leftrightarrow2^n=4\\ \Leftrightarrow2^n=2^2\\ \Leftrightarrow n=2\)

\(2,\left(\dfrac{2}{3}x-\dfrac{1}{3}\right)^5=\dfrac{1}{243}\\ \Leftrightarrow\left(\dfrac{2}{3}x-\dfrac{1}{3}\right)^5=\left(\dfrac{1}{3}\right)^5\\ \Leftrightarrow\dfrac{2}{3}x-\dfrac{1}{3}=\dfrac{1}{3}\\ \Leftrightarrow\dfrac{2}{3}x=\dfrac{1}{3}+\dfrac{1}{3}=\dfrac{2}{3}\\ \Leftrightarrow x=\dfrac{2}{3}:\dfrac{2}{3}=1\)

\(4,\left(2x-1\right)^{10}=49^5\\ \Leftrightarrow\left(2x-1\right)^{10}=\left(7^2\right)^5\\ \Leftrightarrow\left(2x-1\right)^{10}=7^{10}\\ \Leftrightarrow2x-1=7\\ \Leftrightarrow2x=8\\ \Leftrightarrow x=4\)

\(5,x:5^2=\left(\dfrac{3}{5}\right)^2:3^2\\ \Leftrightarrow x:5^2=\dfrac{9}{25}:9\\ \Leftrightarrow x:25-\dfrac{1}{25}\\ \Leftrightarrow x=\dfrac{1}{25}\times25=1\)

\(8,\left(2x-5\right)^4=-81\)

Xem lại đề nhé số mũ chẵn thì phải ra chẵn chứ

Sửa đề \(\left(2x-5\right)^4=81\\ \Leftrightarrow\left(2x-5\right)^4=3^4\\ \Leftrightarrow2x-5=3\\ \Leftrightarrow2x=8\\ \Leftrightarrow x=4\)

Phần bên này mình chỉ làm những câu khác và khó hơn 1 tý thôi còn các câu còn lại bạn có thể tự làm được nhé 

\(1,x:\left(-\dfrac{1}{3}\right)^3=\left(-\dfrac{1}{3}\right)\\ \Leftrightarrow x=\left(-\dfrac{1}{3}\right)\times\left(-\dfrac{1}{3}\right)^3\\ \Leftrightarrow x=\left(-\dfrac{1}{3}\right)^4=\dfrac{1}{81}\\ 2,\left(\dfrac{4}{5}\right)^5.x=\left(\dfrac{4}{5}\right)^7\\ \Leftrightarrow x=\left(\dfrac{4}{5}\right)^7:\left(\dfrac{4}{5}\right)^5=\left(\dfrac{4}{5}\right)^{7-5}=\left(\dfrac{4}{5}\right)^2=\dfrac{16}{25}\)

\(3,\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\\ \Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{1}{4}\\x+\dfrac{1}{2}=-\dfrac{1}{4}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=-\dfrac{3}{4}\end{matrix}\right.\)

\(4,\left(3x+1\right)^3=-27\\ \Leftrightarrow\left(3x+1\right)^3=\left(-3\right)^3\\ \Leftrightarrow3x+1=-3\\ \Leftrightarrow3x=-4\\ \Leftrightarrow x=-\dfrac{4}{3}\)

\(5,\left(\dfrac{1}{2}\right)^2.x=\left(\dfrac{1}{2}\right)^5\\ \Leftrightarrow x=\left(\dfrac{1}{2}\right)^5:\left(\dfrac{1}{2}\right)^2\\ \Leftrightarrow x=\left(\dfrac{1}{2}\right)^{5-2}=\left(\dfrac{1}{2}\right)^3=\dfrac{1}{8}\)

\(6,\left(-\dfrac{1}{3}\right)^3.x=\dfrac{1}{81}\\ \Leftrightarrow\left(-\dfrac{1}{3}\right)^3.x=\left(-\dfrac{1}{3}\right)^4\\ \Leftrightarrow x=\left(-\dfrac{1}{3}\right)^4:\left(-\dfrac{1}{3}\right)^3=-\dfrac{1}{3}\)

\(7,\left(2x-3\right)^2=16\\ \Leftrightarrow\left[{}\begin{matrix}2x-3=4\\2x-3=-4\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)

\(8,\left(x-\dfrac{2}{3}\right)^3=\dfrac{1}{27}\\ \Leftrightarrow\left(x-\dfrac{2}{3}\right)^3=\left(\dfrac{1}{3}\right)^3\\ \Leftrightarrow x-\dfrac{2}{3}=\dfrac{1}{3}\\ \Leftrightarrow x=\dfrac{1}{3}+\dfrac{2}{3}=\dfrac{3}{3}=1\)

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