Let's fill in the missing information for each expression in the table step by step.
1. Expression: [tex]$-\frac{\sqrt{3}}{3} h^4 k^5$[/tex]
- Signo: This expression has a negative sign, so the sign is `-`.
- Coeficiente: The coefficient is [tex]$\frac{\sqrt{3}}{3}$[/tex].
- Parte Literal: The literal part is [tex]$h^4 k^5$[/tex].
- Grado Absoluto: The absolute degree is calculated as the sum of the exponents of the variables: [tex]\(4 (for \ h) + 5 (for \ k) = 9\)[/tex].
2. Expression: [tex]$a b c$[/tex]
- Signo: This expression has a positive sign, so the sign is `+`.
- Coeficiente: The coefficient of the variables [tex]$a$[/tex], [tex]$b$[/tex], and [tex]$c$[/tex] is 1 (since no coefficient is explicitly stated, it is assumed to be 1).
- Parte Literal: The literal part is [tex]$a b c$[/tex].
- Grado Absoluto: The absolute degree is calculated as the sum of the exponents of the variables: [tex]\(1 (for \ a) + 1 (for \ b) + 1 (for \ c) = 3\)[/tex].
3. Expression: [tex]$\frac{x y^2}{4}$[/tex]
- Signo: This expression has a positive sign, so the sign is `+`.
- Coeficiente: The coefficient is [tex]$\frac{1}{4}$[/tex].
- Parte Literal: The literal part is [tex]$x y^2$[/tex].
- Grado Absoluto: The absolute degree is calculated as the sum of the exponents of the variables: [tex]\(1 (for \ x) + 2 (for \ y) = 3\)[/tex].
4. Expression: [tex]$-8 a^4 c^2 d^3$[/tex]
- Signo: This expression has a negative sign, so the sign is `-`.
- Coeficiente: The coefficient is 8.
- Parte Literal: The literal part is [tex]$a^4 c^2 d^3$[/tex].
- Grado Absoluto: The absolute degree is calculated as the sum of the exponents of the variables: [tex]\(4 (for \ a) + 2 (for \ c) + 3 (for \ d) = 9\)[/tex].
Now, we can fill in the table with the correct information.
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
Expresión & Signo & Coeficiente & \begin{tabular}{c}
Parte \\
Literal
\end{tabular} & \begin{tabular}{c}
Grado \\
Absoluto
\end{tabular} \\
\hline
$-\frac{\sqrt{3}}{3} h^4 k^5$ & - & $\frac{\sqrt{3}}{3}$ & $h^4 k^5$ & 9 \\
\hline
$a b c$ & + & 1 & $a b c$ & 3 \\
\hline
$\frac{x y^2}{4}$ & + & $\frac{1}{4}$ & $x y^2$ & 3 \\
\hline
$-8 a^4 c^2 d^3$ & - & 8 & $a^4 c^2 d^3$ & 9 \\
\hline
\end{tabular}
\][/tex]
This completes the table with all the necessary information for each expression.
