2:
a: \(\left(\dfrac{1}{3}\right)^m=\dfrac{1}{81}\)
=>\(\left(\dfrac{1}{3}\right)^m=\left(\dfrac{1}{3}\right)^4\)
=>m=4
b: \(\dfrac{1}{9}\cdot27^n=3^n\)
=>\(\left(\dfrac{3}{27}\right)^n=\dfrac{1}{9}\)
=>\(\left(\dfrac{1}{9}\right)^n=\dfrac{1}{9}\)
=>n=1
c: \(\dfrac{8}{2^n}=2\)
=>\(2^n=\dfrac{8}{2}=4\)
=>n=2
d: \(32^n\cdot16^{-n}=1024\)
=>\(\left(2^5\right)^n\cdot\left(2^4\right)^{-n}=1024\)
=>\(2^{5n-4n}=1024\)
=>\(2^n=2^{10}\)
=>n=10
e: \(3^n\cdot3^{-1}+5\cdot3^{n-1}=162\)
=>\(6\cdot3^{n-1}=162\)
=>\(3^n=\dfrac{162}{2}=81=3^4\)
=>n=4
f: \(\left(n-\dfrac{2}{3}\right)^3=\dfrac{1}{27}\)
=>\(\left(n-\dfrac{2}{3}\right)^3=\left(\dfrac{1}{3}\right)^3\)
=>n-2/3=1/3
=>n=1
