1. **State the problem:** Simplify the expression $$\frac{8x^6}{x^5}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing terms with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule to the expression:** $$\frac{8x^6}{x^5} = 8 \times \frac{x^6}{x^5} = 8x^{6-5}$$ 4. **Simplify the exponent:** $$8x^{\cancel{6-5}} = 8x^1 = 8x$$ 5. **Final answer:** $$8x$$ This means the original expression simplifies to 8 times x.