Simplify the expression. Write the result using positive exponents only. \[ \left(\frac{x^{-4} y^{4}}{x^{3} y^{8}}\right)^{3} \]

To simplify the expression \(\left(\frac{x^{-4} y^{4}}{x^{3} y^{8}}\right)^{3}\) and express it with positive exponents, follow these steps: 1. **Simplify the Inside of the Parentheses:** \[ \frac{x^{-4} y^{4}}{x^{3} y^{8}} = x^{-4 - 3} \cdot y^{4 - 8} = x^{-7} y^{-4} \] 2. **Apply the Exponent Outside the Parentheses:** \[ \left(x^{-7} y^{-4}\right)^3 = x^{-21} y^{-12} \] 3. **Rewrite with Positive Exponents:** \[ x^{-21} y^{-12} = \frac{1}{x^{21} y^{12}} \] So, the simplified expression with positive exponents is: \[ \frac{1}{x^{21} y^{12}} \] **Answer:** \[\frac{1}{\,x^{21}\, y^{12}\,}\]