Answer
$P_1=b^{-40/3}$
$P_2=20b^{-37/3}$
$P_3=190b^{-34/3}$
Work Step by Step
Step 1. With the Binomial Theorem, the $r$th term of the expansion of $(a+b)^n$ is given by:
$\begin{pmatrix} n\\r-1 \end{pmatrix}a^{n-r+1}b^{r-1}$
Step 2. With $n=20, r=1,2,3$, with have the first three terms as:
$P_1=\begin{pmatrix} 20\\1-1 \end{pmatrix}(b^{-2/3})^{20-1+1}(b^{1/3})^{1-1}=b^{-40/3}b^{0}=b^{-40/3}$
$P_2=\begin{pmatrix} 20\\2-1 \end{pmatrix}(b^{-2/3})^{20-2+1}(b^{1/3})^{2-1}=20b^{-38/3}b^{1/3}=20b^{-37/3}$
$P_3=\begin{pmatrix} 20\\3-1 \end{pmatrix}(b^{-2/3})^{20-3+1}(b^{1/3})^{3-1}=190b^{-36/3}b^{2/3}=190b^{-34/3}$
