\( \begin{array}{ll}\text { Math-Homework - Name } \\ (-1)^{3}=-1 & \text { 4. }(-1)^{21}= \\ (-1)^{6}= & \text { 5. }(-1)^{200}= \\ (1)^{7}= & \text { 6. } 1^{54}=\end{array} \)

Let's evaluate each expression step by step. 1. **For \( (-1)^{21} \)**: - The base is \(-1\) and the exponent is odd (21). - When \(-1\) is raised to an odd power, the result is \(-1\). - Therefore, \( (-1)^{21} = -1 \). 2. **For \( (-1)^{6} \)**: - The base is \(-1\) and the exponent is even (6). - When \(-1\) is raised to an even power, the result is \(1\). - Therefore, \( (-1)^{6} = 1 \). 3. **For \( (-1)^{200} \)**: - The base is \(-1\) and the exponent is even (200). - Again, when \(-1\) is raised to an even power, the result is \(1\). - Therefore, \( (-1)^{200} = 1 \). 4. **For \( 1^{7} \)**: - The base is \(1\) and the exponent is \(7\). - Any number raised to any power is itself, so \(1^{7} = 1\). 5. **For \( 1^{54} \)**: - The base is \(1\) and the exponent is \(54\). - Similarly, \(1^{54} = 1\). Now, let's summarize the results: - \( (-1)^{21} = -1 \) - \( (-1)^{6} = 1 \) - \( (-1)^{200} = 1 \) - \( 1^{7} = 1 \) - \( 1^{54} = 1 \) Thus, the completed math homework is: \[ \begin{array}{ll} \text{Math-Homework - Name} \\ (-1)^{3} = -1 & \text{4. } (-1)^{21} = -1 \\ (-1)^{6} = 1 & \text{5. } (-1)^{200} = 1 \\ (1)^{7} = 1 & \text{6. } 1^{54} = 1 \\ \end{array} \]