To solve the expression [tex]\(-3^2 \cdot (0.5)^2 \cdot \left(-\frac{2}{3}\right)^2\)[/tex], we'll break it down into steps and handle each term individually before combining the results.
1. Evaluate the first term: [tex]\(-3^2\)[/tex]
- When you square [tex]\(-3\)[/tex], which gives [tex]\((-3) \cdot (-3)\)[/tex].
[tex]\[
(-3) \cdot (-3) = 9
\][/tex]
So, [tex]\(-3^2 = 9\)[/tex].
2. Evaluate the second term: [tex]\((0.5)^2\)[/tex]
- Squaring 0.5 gives [tex]\(0.5 \cdot 0.5\)[/tex].
[tex]\[
0.5 \cdot 0.5 = 0.25
\][/tex]
So, [tex]\((0.5)^2 = 0.25\)[/tex].
3. Evaluate the third term: [tex]\(\left(-\frac{2}{3}\right)^2\)[/tex]
- Squaring [tex]\(-\frac{2}{3}\)[/tex] means [tex]\(\left(-\frac{2}{3}\right) \cdot \left(-\frac{2}{3}\right)\)[/tex].
[tex]\[
\left(-\frac{2}{3}\right) \cdot \left(-\frac{2}{3}\right) = \frac{4}{9} \approx 0.4444\ldots
\][/tex]
So, [tex]\(\left(-\frac{2}{3}\right)^2 = \frac{4}{9} \approx 0.4444\ldots\)[/tex].
4. Combine the results:
- Now, we need to multiply all three results together: [tex]\(9 \cdot 0.25 \cdot 0.4444\ldots\)[/tex].
[tex]\[
9 \cdot 0.25 = 2.25
\][/tex]
[tex]\[
2.25 \cdot 0.4444\ldots = 1.0
\][/tex]
Therefore, the value of the expression [tex]\(-3^2 \cdot (0.5)^2 \cdot \left(-\frac{2}{3}\right)^2\)[/tex] is [tex]\(1.0\)[/tex].
