To simplify the expression [tex]\( 3 \cdot 2^3 \cdot 2 \cdot 3^2 \)[/tex], follow these steps:
1. Compute the value of [tex]\(2^3\)[/tex].
- [tex]\(2^3 = 2 \times 2 \times 2 = 8\)[/tex]
2. Multiply the value obtained from step 1 by 2.
- [tex]\(8 \times 2 = 16\)[/tex]
3. Compute the value of [tex]\(3^2\)[/tex].
- [tex]\(3^2 = 3 \times 3 = 9\)[/tex]
4. Now multiply the constants and the results from the earlier steps together in the order given in the expression:
- [tex]\(3 \times 16 \times 9\)[/tex]
5. Proceed by multiplying from left to right:
- [tex]\(3 \times 16 = 48\)[/tex]
- [tex]\(48 \times 9 = 432\)[/tex]
Therefore, the simplified expression [tex]\( 3 \cdot 2^3 \cdot 2 \cdot 3^2 \)[/tex] equals [tex]\( 432 \)[/tex].
The correct answer is:
B. 432
