\(a)3^2.\left(x+4\right)-5^2=5.22.\\ \Leftrightarrow9.\left(x+4\right)-25=110.\\ \Leftrightarrow9.\left(x+4\right)=135.\\ \Leftrightarrow x=11.\\ b)4\left(x^2-4\right)=7^2-1^{10}.\\ \Leftrightarrow4\left(x^2-4\right)=49-1.\\ \Leftrightarrow4\left(x^2-4\right)=48.\\ \Leftrightarrow x^2-4=12.\\ \Leftrightarrow x^2=16.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4.\\x=-4.\end{matrix}\right.\)
\(c)5x+x=39-3^{11}:3^9.\\ \Leftrightarrow6x=39-3^2.\\ \Leftrightarrow6x=30.\\ \Leftrightarrow x=5.\)
\(d)\left(3^2-2^3\right)x+3^2.2^2=4^2.3.\\ \Leftrightarrow\left(9-8\right)x+9.4=16.3.\\ \Leftrightarrow x+36=48.\\ \Leftrightarrow x=12.\)
\(e)\left(x-2\right)^3=64.\\ \Leftrightarrow\left(x-2\right)^3=4^3.\\ \Leftrightarrow x-2=4.\\ \Leftrightarrow x=6.\)
\(f)\left(2x+1\right)^4=81.\\ \Leftrightarrow\left[{}\begin{matrix}(2x+1)^4=3^4.\\(2x+1)^4=\left(-3\right)^4.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+1=3.\\2x+1=-3.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1.\\x=-2.\end{matrix}\right.\)
\(g)x^3-x=0.\\ \Leftrightarrow x\left(x^2-1\right)=0.\\ \Leftrightarrow x\left(x-1\right)\left(x+1\right)=0.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0.\\x=1.\\x=-1.\end{matrix}\right.\)
