To simplify the given expression [tex]\(\left(-3 \times 10^2\right)^2\)[/tex], let's follow the steps in detail:
1. Evaluate the expression inside the parentheses:
- First, calculate [tex]\(10^2\)[/tex]. Since [tex]\(10^2 = 100\)[/tex], we have:
[tex]\[
-3 \times 10^2 = -3 \times 100
\][/tex]
2. Multiply the constants:
- Now, multiply [tex]\(-3\)[/tex] by [tex]\(100\)[/tex]:
[tex]\[
-3 \times 100 = -300
\][/tex]
3. Square the result of the multiplication:
- Finally, square [tex]\(-300\)[/tex]:
[tex]\[
(-300)^2
\][/tex]
- Squaring [tex]\(-300\)[/tex] involves multiplying [tex]\(-300\)[/tex] by itself:
[tex]\[
-300 \times -300 = 90000
\][/tex]
Therefore, the simplified result of [tex]\(\left(-3 \times 10^2\right)^2\)[/tex] is [tex]\(\boxed{90000}\)[/tex].
