Let's evaluate each of the expressions step-by-step:
1. Evaluate [tex]\(5^0 + 2^1\)[/tex]:
[tex]\[
5^0 = 1 \quad \text{(Any non-zero number to the power of zero is 1)}
\][/tex]
[tex]\[
2^1 = 2 \quad \text{(Any number to the power of one is itself)}
\][/tex]
Hence:
[tex]\[
5^0 + 2^1 = 1 + 2 = 3
\][/tex]
2. Evaluate [tex]\(2^0 + 1^1\)[/tex]:
[tex]\[
2^0 = 1 \quad \text{(Any non-zero number to the power of zero is 1)}
\][/tex]
[tex]\[
1^1 = 1 \quad \text{(Any number to the power of one is itself)}
\][/tex]
Hence:
[tex]\[
2^0 + 1^1 = 1 + 1 = 2
\][/tex]
3. Evaluate [tex]\(2^0 + 2^1\)[/tex]:
[tex]\[
2^0 = 1 \quad \text{(Any non-zero number to the power of zero is 1)}
\][/tex]
[tex]\[
2^1 = 2 \quad \text{(Any number to the power of one is itself)}
\][/tex]
Hence:
[tex]\[
2^0 + 2^1 = 1 + 2 = 3
\][/tex]
4. Evaluate [tex]\(6^0 - 3^0\)[/tex]:
[tex]\[
6^0 = 1 \quad \text{(Any non-zero number to the power of zero is 1)}
\][/tex]
[tex]\[
3^0 = 1 \quad \text{(Any non-zero number to the power of zero is 1)}
\][/tex]
Hence:
[tex]\[
6^0 - 3^0 = 1 - 1 = 0
\][/tex]
5. Evaluate [tex]\(6^0 - 6^1\)[/tex]:
[tex]\[
6^0 = 1 \quad \text{(Any non-zero number to the power of zero is 1)}
\][/tex]
[tex]\[
6^1 = 6 \quad \text{(Any number to the power of one is itself)}
\][/tex]
Hence:
[tex]\[
6^0 - 6^1 = 1 - 6 = -5
\][/tex]
Therefore, comparing all the values:
- [tex]\(5^0 + 2^1 = 3\)[/tex]
- [tex]\(2^0 + 1^1 = 2\)[/tex]
- [tex]\(2^0 + 2^1 = 3\)[/tex]
- [tex]\(6^0 - 3^0 = 0\)[/tex]
- [tex]\(6^0 - 6^1 = -5\)[/tex]
The expression that is equal to [tex]\(5^0 + 2^1\)[/tex] is [tex]\(2^0 + 2^1\)[/tex].
