Bài 1:

a) \(\left(4x-\dfrac{1}{3}\right)^6=1\)

\(\Rightarrow4x-\dfrac{1}{3}=1\)

\(4x=1+\dfrac{1}{3}\)

\(4x=\dfrac{4}{3}\)

\(x=\dfrac{4}{3}:4\)

\(x=\dfrac{1}{3}\)

b) \(\left(5x-\dfrac{2}{3}\right)^2=0\)

\(\Rightarrow5x-\dfrac{2}{3}=0\)

\(5x=\dfrac{2}{3}\)

\(x=\dfrac{2}{3}:5\)

\(x=\dfrac{2}{15}\)

c) \(\left(\dfrac{1}{3}x-\dfrac{1}{2}\right)^3=-8\)

\(\Rightarrow\left(\dfrac{1}{3}x-\dfrac{1}{2}\right)^3=\left(-2\right)^3\)

\(\dfrac{1}{3}x-\dfrac{1}{2}=-2\)

\(\dfrac{1}{3}x=-2+\dfrac{1}{2}\)

\(\dfrac{1}{3}x=\dfrac{-3}{2}\)

\(x=\dfrac{-3}{2}:\dfrac{1}{3}\)

\(x=\dfrac{-9}{2}\)

d) \(\dfrac{81}{3^n}=3\)

\(\Rightarrow\dfrac{3^4}{3^n}=3\)

\(\Rightarrow3^n.3=3^4\)

\(3^{n+1}=3^4\)

n + 1 = 4

n = 4 - 1

n = 3

e) \(\dfrac{\left(-2\right)^x}{64}=-2\)

\(\Rightarrow\dfrac{\left(-2\right)^x}{\left(-2\right)^6}=-2\)

\(\Rightarrow\left(-2\right)^x=\left(-2\right)^6.\left(-2\right)\)

\(\left(-2\right)^x=\left(-2\right)^7\)

x = 7

f) (-20)n : 10n = 16

(-20 : 10)n = 16

(-2)n = 16

(-2)n = (-2)4

n = 4.