To simplify the expression [tex]\(\left(4 x^3 y^2 z^4\right)\left(2 x^3 y^4 z^3\right)\)[/tex], follow these steps:
1. Multiply the coefficients:
- The coefficients in the terms are [tex]\(4\)[/tex] and [tex]\(2\)[/tex].
- [tex]\(4 \times 2 = 8\)[/tex].
2. Add the exponents for each variable:
- For [tex]\(x\)[/tex]: The exponents are [tex]\(3\)[/tex] and [tex]\(3\)[/tex]. Adding them, we get [tex]\(3 + 3 = 6\)[/tex].
- For [tex]\(y\)[/tex]: The exponents are [tex]\(2\)[/tex] and [tex]\(4\)[/tex]. Adding them, we get [tex]\(2 + 4 = 6\)[/tex].
- For [tex]\(z\)[/tex]: The exponents are [tex]\(4\)[/tex] and [tex]\(3\)[/tex]. Adding them, we get [tex]\(4 + 3 = 7\)[/tex].
Therefore, the simplified expression is:
[tex]\[8 x^6 y^6 z^7\][/tex]
So, the correct option is:
[tex]\[8 x^6 y^6 z^7\][/tex]
