Answer
$b^{-40/3}; 20b^{-37/3};190b^{-34/3};$
Work Step by Step
The $k+1$th term of the expansion of $(x+y)^n$ is:
$$T_{k+1}=\binom{n}{k}x^{n-k}y^k,\text{ where }k=0,1,2,\dots,n.\tag1$$
We find the terms on the positions $1$, $2$ and $3$ of the expansion of $(b^{-2/3}+b^{1/3})^{20}$ by substituting $k=0,1,2$, $n=20$ in Eq.$(1)$:
$$\begin{align*}
T_{1}&=\binom{20}{0}(b^{-2/3})^20=b^{-40/3}\\
T_{2}&=\binom{20}{1}(b^{-2/3})^19b^{1/3}=20b^{-38/3}b^{1/3}=20b^{-37/3}\\
T_{3}&=\binom{20}{2}(b^{-2/3})^18(b^{1/3})^2=190b^{-12}b^{2/3}=190b^{-34/3}.
\end{align*}$$
Therefore the first three terms are $b^{-40/3}, 20b^{-37/3},190b^{-34/3}$.
