To complete the table, let's follow the pattern of how the expressions are expanded and the results calculated.
- Expression:
- \(4^3\) is expanded as \(4 \cdot 4 \cdot 4\), which results in \(64\).
- \(4^2\) is expanded as \(4 \cdot 4\), which results in \(16\).
- \(4^1\) will be \(4\), which can be represented as \(4\).
- \(4^0\) is \(1\), and can be expanded as \(1\).
- \(4^{-1}\) is \(1/4\), which is expressed as \(1/4\).
- \(4^{-2}\) is \(1/(4 \cdot 4)\) which is \(1/16\).
Now, let's fill in the blanks:
- For \(4^1\): the expanded form is \(4\), and the result is \(4\).
- For \(4^0\): the expanded form is \(1\), and the result is \(1\).
- For \(4^{-1}\): the expanded form is \(1/4\), and the result is \(1/4 = 0.25\).
- For \(4^{-2}\): the expanded form is \(1/(4 \cdot 4)\), and the result is \(1/16\).
Now, filling in the table:
- Expression: \(4^3\), \(4^2\), \(4^1\), \(4^0\), \(4^{-1}\), \(4^{-2}\)
- Expanded: \(4 \cdot 4 \cdot 4\), \(4 \cdot 4\), \(4\), \(1\), \(1/4\), \(1/(4 \cdot 4)\)
- Result: \(64\), \(16\), \(4\), \(1\), \(1/4\), \(1/16\)
So the table is completed as follows:
- Expanded: \(4 \cdot 4 \cdot 4\), \(4 \cdot 4\), \(4\), \(1\), \(1/4\), \(1/(4 \cdot 4)\)
- Result: \(64\), \(16\), \(4\), \(1\), \(1/4\), \(1/16\)