1. **State the problem:** Simplify the expression $$\left(\frac{x^{5}y^{-3}z}{xyz}\right)^{-1}$$. 2. **Recall the rules:** - When dividing powers with the same base, subtract the exponents: $$a^{m} \div a^{n} = a^{m-n}$$. - Negative exponents mean reciprocal: $$a^{-n} = \frac{1}{a^{n}}$$. - The power of a quotient rule: $$\left(\frac{a}{b}\right)^{-1} = \frac{b}{a}$$. 3. **Simplify inside the parentheses first:** $$\frac{x^{5}y^{-3}z}{xyz} = x^{5-1} y^{-3-1} z^{1-1} = x^{4} y^{-4} z^{0}$$ 4. **Simplify powers:** Since $$z^{0} = 1$$, the expression inside parentheses becomes: $$x^{4} y^{-4}$$ 5. **Apply the outer exponent -1:** $$\left(x^{4} y^{-4}\right)^{-1} = x^{-4} y^{4}$$ 6. **Rewrite with positive exponents:** $$x^{-4} y^{4} = \frac{y^{4}}{x^{4}}$$ **Final answer:** $$\frac{y^{4}}{x^{4}}$$