Answer :
Let's fill in the table by calculating each power step by step.
[tex]\[ \begin{tabular}{|l|l|l|l|} \hline & \text{BASE} & \text{EXPONENTE} & \text{POTENCIA} \\ \hline 10^3 & 10 & 3 & 1000 \\ \hline (-5)^4 & -5 & 4 & 625 \\ \hline (-2)^5 & -2 & 5 & -32 \\ \hline 6^3 & 6 & 3 & 216 \\ \hline (-7)^2 & -7 & 2 & 49 \\ \hline (-3)^3 & -3 & 3 & -27 \\ \hline \end{tabular} \][/tex]
### Detailed Explanation
1. Calculating \(10^3\):
- Base: \(10\)
- Exponent: \(3\)
- Calculation: \(10 \times 10 \times 10 = 1000\)
[tex]\[ 10^3 = 1000 \][/tex]
2. Calculating \((-5)^4\):
- Base: \(-5\)
- Exponent: \(4\)
- Calculation: \((-5) \times (-5) \times (-5) \times (-5) = 25 \times 25 = 625\)
[tex]\[ (-5)^4 = 625 \][/tex]
3. Calculating \((-2)^5\):
- Base: \(-2\)
- Exponent: \(5\)
- Calculation: \((-2) \times (-2) \times (-2) \times (-2) \times (-2) = -32\)
[tex]\[ (-2)^5 = -32 \][/tex]
4. Calculating \(6^3\):
- Base: \(6\)
- Exponent: \(3\)
- Calculation: \(6 \times 6 \times 6 = 216\)
[tex]\[ 6^3 = 216 \][/tex]
5. Calculating \((-7)^2\):
- Base: \(-7\)
- Exponent: \(2\)
- Calculation: \((-7) \times (-7) = 49\)
[tex]\[ (-7)^2 = 49 \][/tex]
6. Calculating \((-3)^3\):
- Base: \(-3\)
- Exponent: \(3\)
- Calculation: \((-3) \times (-3) \times (-3) = -27\)
[tex]\[ (-3)^3 = -27 \][/tex]
After calculating each of these, we fill in the table with the values obtained.
[tex]\[ \begin{tabular}{|l|l|l|l|} \hline & \text{BASE} & \text{EXPONENTE} & \text{POTENCIA} \\ \hline 10^3 & 10 & 3 & 1000 \\ \hline (-5)^4 & -5 & 4 & 625 \\ \hline (-2)^5 & -2 & 5 & -32 \\ \hline 6^3 & 6 & 3 & 216 \\ \hline (-7)^2 & -7 & 2 & 49 \\ \hline (-3)^3 & -3 & 3 & -27 \\ \hline \end{tabular} \][/tex]
### Detailed Explanation
1. Calculating \(10^3\):
- Base: \(10\)
- Exponent: \(3\)
- Calculation: \(10 \times 10 \times 10 = 1000\)
[tex]\[ 10^3 = 1000 \][/tex]
2. Calculating \((-5)^4\):
- Base: \(-5\)
- Exponent: \(4\)
- Calculation: \((-5) \times (-5) \times (-5) \times (-5) = 25 \times 25 = 625\)
[tex]\[ (-5)^4 = 625 \][/tex]
3. Calculating \((-2)^5\):
- Base: \(-2\)
- Exponent: \(5\)
- Calculation: \((-2) \times (-2) \times (-2) \times (-2) \times (-2) = -32\)
[tex]\[ (-2)^5 = -32 \][/tex]
4. Calculating \(6^3\):
- Base: \(6\)
- Exponent: \(3\)
- Calculation: \(6 \times 6 \times 6 = 216\)
[tex]\[ 6^3 = 216 \][/tex]
5. Calculating \((-7)^2\):
- Base: \(-7\)
- Exponent: \(2\)
- Calculation: \((-7) \times (-7) = 49\)
[tex]\[ (-7)^2 = 49 \][/tex]
6. Calculating \((-3)^3\):
- Base: \(-3\)
- Exponent: \(3\)
- Calculation: \((-3) \times (-3) \times (-3) = -27\)
[tex]\[ (-3)^3 = -27 \][/tex]
After calculating each of these, we fill in the table with the values obtained.
