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

Question

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

UpStudy AI · Accepted Answer

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:

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

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

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