Sure, let's determine whether each equation is true or false.
1. Evaluating the first equation [tex]\(2^4 = 2 \times 4\)[/tex]:
- On the left-hand side, [tex]\(2^4\)[/tex] means [tex]\(2\)[/tex] raised to the power of [tex]\(4\)[/tex], which equals [tex]\(16\)[/tex].
- On the right-hand side, [tex]\(2 \times 4\)[/tex] equals [tex]\(8\)[/tex].
- Comparing both sides: [tex]\(16 \neq 8\)[/tex].
- Thus, the equation [tex]\(2^4 = 2 \times 4\)[/tex] is False.
2. Evaluating the second equation [tex]\(2^4 = 4 + 4\)[/tex]:
- On the left-hand side, [tex]\(2^4\)[/tex] means [tex]\(2\)[/tex] raised to the power of [tex]\(4\)[/tex], which again equals [tex]\(16\)[/tex].
- On the right-hand side, [tex]\(4 + 4\)[/tex] equals [tex]\(8\)[/tex].
- Comparing both sides: [tex]\(16 \neq 8\)[/tex].
- Thus, the equation [tex]\(2^4 = 4 + 4\)[/tex] is False.
3. Evaluating the third equation [tex]\(2^4 = 2 \times 2 \times 2 \times 2\)[/tex]:
- On the left-hand side, [tex]\(2^4\)[/tex] means [tex]\(2\)[/tex] raised to the power of [tex]\(4\)[/tex], which equals [tex]\(16\)[/tex].
- On the right-hand side, [tex]\(2 \times 2 \times 2 \times 2\)[/tex] equals [tex]\(16\)[/tex] (since [tex]\(2 \times 2 = 4\)[/tex], and [tex]\(4 \times 2 = 8\)[/tex], and [tex]\(8 \times 2 = 16\)[/tex]).
- Comparing both sides: [tex]\(16 = 16\)[/tex].
- Thus, the equation [tex]\(2^4 = 2 \times 2 \times 2 \times 2\)[/tex] is True.
To summarize:
[tex]\[
\begin{array}{l}
2^4 = 2 \times 4 \quad \text{False} \\
2^4 = 4 + 4 \quad \text{False} \\
2^4 = 2 \times 2 \times 2 \times 2 \quad \text{True}
\end{array}
\][/tex]
