Question: User: 5x³.x⁷
1. **State the problem:** Simplify the expression $5x^3 \cdot x^7$.
2. **Recall the rule for multiplying powers with the same base:** When multiplying terms with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$
3. **Apply the rule:** Here, the base is $x$, and the exponents are $3$ and $7$. So,
$$5x^3 \cdot x^7 = 5x^{3+7}$$
4. **Simplify the exponent:**
$$5x^{10}$$
5. **Final answer:** The simplified expression is $5x^{10}$.