Let's solve each given mathematical expression step by step and see which one is equal to [tex]\(5^0 + 2^1\)[/tex].
1. Calculating [tex]\(5^0 + 2^1\)[/tex]:
- [tex]\(5^0 = 1\)[/tex] since any number to the power of 0 is 1.
- [tex]\(2^1 = 2\)[/tex].
- So, [tex]\(5^0 + 2^1 = 1 + 2 = 3\)[/tex].
Now, let's evaluate the other expressions to see which one matches 3.
2. Calculating [tex]\(2^0 + 1^1\)[/tex]:
- [tex]\(2^0 = 1\)[/tex] since any number to the power of 0 is 1.
- [tex]\(1^1 = 1\)[/tex].
- So, [tex]\(2^0 + 1^1 = 1 + 1 = 2\)[/tex].
- This result is 2, which is not equal to 3.
3. Calculating [tex]\(6^0 - 6^1\)[/tex]:
- [tex]\(6^0 = 1\)[/tex] since any number to the power of 0 is 1.
- [tex]\(6^1 = 6\)[/tex].
- So, [tex]\(6^0 - 6^1 = 1 - 6 = -5\)[/tex].
- This result is -5, which is not equal to 3.
4. Calculating [tex]\(2^0 + 2^1\)[/tex]:
- [tex]\(2^0 = 1\)[/tex] since any number to the power of 0 is 1.
- [tex]\(2^1 = 2\)[/tex].
- So, [tex]\(2^0 + 2^1 = 1 + 2 = 3\)[/tex].
- This result is 3, which is equal to [tex]\(5^0 + 2^1\)[/tex].
5. Calculating [tex]\(6^0 - 3^0\)[/tex]:
- [tex]\(6^0 = 1\)[/tex] since any number to the power of 0 is 1.
- [tex]\(3^0 = 1\)[/tex].
- So, [tex]\(6^0 - 3^0 = 1 - 1 = 0\)[/tex].
- This result is 0, which is not equal to 3.
Therefore, among the given options, [tex]\(2^0 + 2^1\)[/tex] (which equals 3) is the expression that is equal to [tex]\(5^0 + 2^1\)[/tex].
