To simplify the expression [tex]\(\left(6 w^8\right)\left(3 w^4\right)\left(4 w^3\right)\)[/tex], we can break it down into two main steps: handling the coefficients (numerical parts) and handling the exponents of [tex]\(w\)[/tex].
1. Simplify the Coefficients:
- We need to multiply the coefficients together: [tex]\(6\)[/tex], [tex]\(3\)[/tex], and [tex]\(4\)[/tex].
- Calculation: [tex]\(6 \cdot 3 \cdot 4 = 72\)[/tex].
2. Simplify the Exponents:
- We need to apply the properties of exponents to the powers of [tex]\(w\)[/tex].
- When multiplying terms with the same base, we add their exponents: [tex]\(w^8\)[/tex], [tex]\(w^4\)[/tex], and [tex]\(w^3\)[/tex].
- Calculation: [tex]\(8 + 4 + 3 = 15\)[/tex].
Putting these results together, we get:
[tex]\[
\left(6 w^8\right)\left(3 w^4\right)\left(4 w^3\right) = 72 w^{15}
\][/tex]
So, the simplified expression is:
[tex]\[
72 w^{15}
\][/tex]
