Let's break down the problem step-by-step to determine which expression is equivalent to [tex]\(2^4\)[/tex].
First, understand that [tex]\(2^4\)[/tex] means 2 raised to the power of 4. This is equivalent to multiplying the number 2 by itself four times:
[tex]\[ 2^4 = 2 \cdot 2 \cdot 2 \cdot 2 \][/tex]
Now, we'll compute the result step-by-step:
[tex]\[ 2 \cdot 2 = 4 \][/tex]
[tex]\[ 4 \cdot 2 = 8 \][/tex]
[tex]\[ 8 \cdot 2 = 16 \][/tex]
So, [tex]\(2^4\)[/tex] equals 16.
Now, let's compare this result to the given expressions:
1. [tex]\(2 + 2 + 2 + 2 = 8\)[/tex]
- Adding 2 four times results in 8, which is not equal to 16.
2. [tex]\(2 \cdot 2 \cdot 2 \cdot 2 = 16\)[/tex]
- This multiplication expression exactly matches our computation of [tex]\(2^4\)[/tex].
3. [tex]\(2 \cdot 4 = 8\)[/tex]
- Multiplying 2 by 4 results in 8, which is not equal to 16.
4. [tex]\(4 \cdot 4 = 16\)[/tex]
- While this multiplication results in 16, it is not equivalent to [tex]\(2^4\)[/tex]. The base and the exponent are not the same.
Therefore, the correct and equivalent expression to [tex]\(2^4\)[/tex] is:
[tex]\[ 2 \cdot 2 \cdot 2 \cdot 2 = 16 \][/tex]
