To determine which expression is equivalent to [tex]\(2^5\)[/tex], let's examine each option step-by-step:
1. Option 1: [tex]\(2 \cdot 2 \cdot 2 \cdot 2 \cdot 2\)[/tex]
- This option involves multiplying the number 2 by itself five times.
- The calculation yields [tex]\(2 \cdot 2 = 4\)[/tex], then [tex]\(4 \cdot 2 = 8\)[/tex], followed by [tex]\(8 \cdot 2 = 16\)[/tex], and finally [tex]\(16 \cdot 2 = 32\)[/tex].
- Therefore, [tex]\(2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 32\)[/tex].
2. Option 2: [tex]\(2 \cdot 5\)[/tex]
- This option involves multiplying 2 and 5.
- The calculation is [tex]\(2 \cdot 5 = 10\)[/tex].
- Therefore, [tex]\(2 \cdot 5 = 10\)[/tex].
3. Option 3: [tex]\(2 + 2 + 2 + 2 + 2\)[/tex]
- This option involves adding the number 2 five times.
- The calculation is [tex]\(2 + 2 + 2 + 2 + 2\)[/tex], which equals [tex]\(10\)[/tex].
- Therefore, [tex]\(2 + 2 + 2 + 2 + 2 = 10\)[/tex].
4. Option 4: [tex]\(5 \cdot 5\)[/tex]
- This option involves multiplying 5 by itself.
- The calculation is [tex]\(5 \cdot 5 = 25\)[/tex].
- Therefore, [tex]\(5 \cdot 5 = 25\)[/tex].
After evaluating each option, the one that corresponds to the value of [tex]\(2^5\)[/tex] is:
- Option 1: [tex]\(2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 32\)[/tex].
Therefore, the correct choice is the first option as it accurately represents [tex]\(2^5\)[/tex].
