a) 4ⁿ=256

=>4ⁿ=4⁴

=>n=4

b) 6²⁰.6⁴ⁿ=6²⁰⁰

=>6²⁰⁺⁴ⁿ=6²⁰⁰

=>20+4n=200

=>4n=200-20

=>4n=180

=>n=180:4

=>n=45

\(\dfrac{1}{3}x+\dfrac{2}{5}\left(x-1\right)=0\)

\(\dfrac{1}{3}x+\dfrac{2}{5}x-\dfrac{2}{5}=0\)

\(\dfrac{1}{3}x+\dfrac{2}{5}x=\dfrac{2}{5}\)

\(x.\left(\dfrac{1}{3}+\dfrac{2}{5}\right)=\dfrac{2}{5}\)

\(x.\dfrac{11}{15}=\dfrac{2}{5}\)

\(x=\dfrac{2}{5}:\dfrac{11}{15}\)

\(x=\dfrac{6}{11}\)