To complete the table, we can follow the pattern established in the columns for the expressions and their corresponding expanded forms and results. Here's the completed table based on the given information:
| Expression | Expanded | Result | |------------|---------------------|-------------| | 4^3 | 4 ⋅ 4 ⋅ 4 | 64 | | 4^2 | 4 ⋅ 4 | 16 | | 4^1 | 4 | 4 | | 4^0 | 1 | 1 | | 4^-1 | 1/4 | 0.25 | | 4^-2 | 1/(4 ⋅ 4) | 1/16 |
Explanation:
- For 4^3, the expression is \(4\) multiplied by itself \(3\) times, giving \(64\).
- For 4^2, it's \(4\) multiplied by itself \(2\) times, giving \(16\).
- For 4^1, it simply equals \(4\).
- For 4^0, any non-zero number raised to the power of \(0\) equals \(1\).
- For 4^-1, it represents the reciprocal of \(4\), which is \(1/4\) or \(0.25\).
- For 4^-2, it is \(1/(4 \cdot 4)\) which equals \(1/16\).
Feel free to watch the video to further enhance your understanding!