c: \(\left(-\frac13\right)^3\cdot x=\frac{1}{81}\)
=>\(x\cdot\frac{-1}{27}=\frac{1}{81}\)
=>\(x=\frac{1}{81}:\frac{-1}{27}=\frac{-27}{81}=-\frac13\)
d: \(\left(\frac45\right)^5\cdot x=\left(\frac45\right)^7\)
=>\(x=\left(\frac45\right)^7:\left(\frac45\right)^5=\left(\frac45\right)^2=\frac{16}{25}\)
e: \(\left(\frac23x-\frac13\right)^5=\frac{1}{243}\)
=>\(\left(\frac23x-\frac13\right)^5=\left(\frac13\right)^5\)
=>\(\frac23x-\frac13=\frac13\)
=>\(\frac23x=\frac23\)
=>x=1
f: \(\left(2x-3\right)^2=16\)
=>\(\left[\begin{array}{l}2x-3=4\\ 2x-3=-4\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=7\\ 2x=-1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac72\\ x=-\frac12\end{array}\right.\)
g: \(\left(x+\frac12\right)^2=\frac{1}{16}\)
=>\(\left[\begin{array}{l}x+\frac12=\frac14\\ x+\frac12=-\frac14\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac14-\frac12=-\frac14\\ x=-\frac14-\frac12=-\frac34\end{array}\right.\)
h: \(\left(\frac25-3x\right)^2=\frac{9}{25}\)
=>\(\left(3x-\frac25\right)^2=\frac{9}{25}\)
=>\(\left[\begin{array}{l}3x-\frac25=\frac35\\ 3x-\frac25=-\frac35\end{array}\right.\Rightarrow\left[\begin{array}{l}3x=\frac25+\frac35=\frac55=1\\ 3x=-\frac35+\frac25=-\frac15\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac13\\ x=-\frac{1}{15}\end{array}\right.\)
i: \(\left(x-\frac23\right)^3=\frac{1}{27}\)
=>\(x-\frac23=\frac13\)
=>\(x=\frac23+\frac13=\frac33=1\)
j: \(\left(x+2\right)^2=25\)
=>\(\left[\begin{array}{l}x+2=5\\ x+2=-5\end{array}\right.\Rightarrow\left[\begin{array}{l}x=5-2=3\\ x=-5-2=-7\end{array}\right.\)
k: \(\left(2x-1\right)^3-27=0\)
=>\(\left(2x-1\right)^3=27\)
=>2x-1=3
=>2x=4
=>x=2
l: \(4^{x-2}=64\)
=>\(4^{x-2}=4^3\)
=>x-2=3
=>x=5
