To determine whether [tex]\((-5) \times (-5) \times (-5) \times (-5)\)[/tex] is equivalent to [tex]\(-5^4\)[/tex], let's examine both expressions step-by-step.
1. Expression [tex]\((-5) \times (-5) \times (-5) \times (-5)\)[/tex]:
- Multiply the first two factors:
[tex]\[
(-5) \times (-5) = 25
\][/tex]
- Next, multiply by the third factor:
[tex]\[
25 \times (-5) = -125
\][/tex]
- Finally, multiply by the fourth factor:
[tex]\[
-125 \times (-5) = 625
\][/tex]
- So, [tex]\((-5) \times (-5) \times (-5) \times (-5) = 625\)[/tex].
2. Expression [tex]\(-5^4\)[/tex]:
- According to the order of operations (exponentiation first), raise [tex]\(5\)[/tex] to the power of [tex]\(4\)[/tex]:
[tex]\[
5^4 = 5 \times 5 \times 5 \times 5 = 625
\][/tex]
- Then, apply the negative sign to the entire result:
[tex]\[
- (5^4) = -625
\][/tex]
Clearly, [tex]\((-5) \times (-5) \times (-5) \times (-5)\)[/tex] equals [tex]\(625\)[/tex] and [tex]\(-5^4\)[/tex] (interpreted as [tex]\(-(5^4)\)[/tex]) equals [tex]\(-625\)[/tex]. These two expressions provide different results.
Thus, the correct answer to the question "[tex]$-5 \times -5 \times -5 \times -5$[/tex] is equivalent to [tex]$-5^4$[/tex] (1 point)" is:
False
