Let's solve the problem step by step:
1. Calculate [tex]\((-3)^2\)[/tex]:
- Squaring a negative number involves multiplying the number by itself. Therefore, [tex]\((-3) \times (-3)\)[/tex] needs to be calculated.
- When you multiply [tex]\(-3\)[/tex] by [tex]\(-3\)[/tex], you get [tex]\(9\)[/tex]. This is because the product of two negative numbers is a positive number.
So, [tex]\((-3)^2 = 9\)[/tex].
2. Compare the result to 32:
- Now, we need to compare the value [tex]\(9\)[/tex] to [tex]\(32\)[/tex].
- We have three possible comparison symbols: [tex]\(>\)[/tex] (greater than), [tex]\(<\)[/tex] (less than), and [tex]\(=\)[/tex] (equal to).
- We observe that [tex]\(9\)[/tex] is less than [tex]\(32\)[/tex].
Therefore, [tex]\(9 < 32\)[/tex].
Putting it all together, [tex]\((-3)^2 = 9\)[/tex], and [tex]\(9\)[/tex] is less than [tex]\(32\)[/tex]. Thus, the correct symbol to use is [tex]\(<\)[/tex].
So, the answer is: [tex]\((-3)^2 < 32\)[/tex].
