[tex]\bf 5y^4+y^3+\frac{2}{3}y^2+y+1\quad
\begin{cases}
5y^4&\textit{degree}\ \boxed{4}\\
y^3&\textit{degree}\ 3\\
\frac{2}{3}y^2&\textit{degree}\ 2\\
y&\textit{degree}\ 1
\end{cases}\quad \textit{polynomial degree, 4}\\\\
-------------------------------\\\\
3a^9+7x^3y^5b^2-8b^3y^6\quad
\begin{cases}
3a^9&\textit{degree}\ 9\\
7x^3y^5b^2&\textit{degree}\ 3+5+2=\boxed{10}\\
8b^3y^6&\textit{degree}\ 3+6=9
\end{cases}
\\\\
\textit{polynomial degree, 10}[/tex]
so.. notice, if the term has several variables, the degree of the term is, the sum of the exponents.