1. **State the problem:** Simplify the expression $$\frac{x^6 z^3}{x^2 z^5}$$. 2. **Recall the rule for dividing powers with the same base:** $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule to each variable separately:** $$\frac{x^6}{x^2} = x^{6-2} = x^4$$ $$\frac{z^3}{z^5} = z^{3-5} = z^{-2}$$ 4. **Write the expression with the simplified powers:** $$x^4 z^{-2}$$ 5. **Rewrite negative exponents as positive by moving the term to the denominator:** $$x^4 \cdot \frac{1}{z^2} = \frac{x^4}{z^2}$$ **Final answer:** $$\frac{x^4}{z^2}$$