At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
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]
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]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.