Connect with a community that values knowledge and expertise on IDNLearn.com. Join our community to receive timely and reliable responses to your questions from knowledgeable professionals.
Sagot :
To determine whether [tex]\((-1)^6\)[/tex] is equivalent to [tex]\(-1 \times -1 \times -1 \times -1 \times -1 \times -1\)[/tex], we need to carefully evaluate the expression step-by-step.
First, let's interpret [tex]\((-1)^6\)[/tex]:
[tex]\[ (-1)^6 \text{ means that } -1 \text{ is multiplied by itself 6 times.} \][/tex]
Now, let's explicitly write out the multiplication:
[tex]\[ (-1) \times (-1) \times (-1) \times (-1) \times (-1) \times (-1) \][/tex]
Next, we can group the multiplications in pairs for easier computation:
[tex]\[ ((-1) \times (-1)) \times ((-1) \times (-1)) \times ((-1) \times (-1)) \][/tex]
We know that multiplying two negative numbers results in a positive number:
[tex]\[ (-1) \times (-1) = 1 \][/tex]
So, substituting back we get:
[tex]\[ 1 \times 1 \times 1 = 1 \][/tex]
Therefore,
[tex]\[ (-1) \times (-1) \times (-1) \times (-1) \times (-1) \times (-1) = 1 \][/tex]
Now we compare this result to [tex]\((-1)^6\)[/tex]:
[tex]\((-1)^6\)[/tex] also simplifies to:
[tex]\[ (-1)^6 = 1 \][/tex]
So, yes, [tex]\((-1)^6 = 1\)[/tex] is equivalent to [tex]\(-1 \times -1 \times -1 \times -1 \times -1 \times -1\)[/tex].
Thus, the statement is \textbf{True}.
First, let's interpret [tex]\((-1)^6\)[/tex]:
[tex]\[ (-1)^6 \text{ means that } -1 \text{ is multiplied by itself 6 times.} \][/tex]
Now, let's explicitly write out the multiplication:
[tex]\[ (-1) \times (-1) \times (-1) \times (-1) \times (-1) \times (-1) \][/tex]
Next, we can group the multiplications in pairs for easier computation:
[tex]\[ ((-1) \times (-1)) \times ((-1) \times (-1)) \times ((-1) \times (-1)) \][/tex]
We know that multiplying two negative numbers results in a positive number:
[tex]\[ (-1) \times (-1) = 1 \][/tex]
So, substituting back we get:
[tex]\[ 1 \times 1 \times 1 = 1 \][/tex]
Therefore,
[tex]\[ (-1) \times (-1) \times (-1) \times (-1) \times (-1) \times (-1) = 1 \][/tex]
Now we compare this result to [tex]\((-1)^6\)[/tex]:
[tex]\((-1)^6\)[/tex] also simplifies to:
[tex]\[ (-1)^6 = 1 \][/tex]
So, yes, [tex]\((-1)^6 = 1\)[/tex] is equivalent to [tex]\(-1 \times -1 \times -1 \times -1 \times -1 \times -1\)[/tex].
Thus, the statement is \textbf{True}.
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. Thank you for visiting IDNLearn.com. For reliable answers to all your questions, please visit us again soon.