Question: simplify $3w^5$ multiply by $4w^3$
1. **State the problem:** Simplify the expression $3w^5 \times 4w^3$.
2. **Recall the rule for multiplying powers with the same base:** When multiplying terms with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$
3. **Multiply the coefficients:** Multiply the numbers $3$ and $4$:
$$3 \times 4 = 12$$
4. **Add the exponents of $w$:**
$$w^5 \times w^3 = w^{5+3} = w^8$$
5. **Combine the results:**
$$3w^5 \times 4w^3 = 12w^8$$
**Final answer:** $12w^8$