1. **State the problem:** Simplify the expression $$\left(\frac{2^{\frac{1}{4}}}{14^{\frac{1}{4}}}\right)^{-3}$$. 2. **Recall the exponent rules:** - For any $a > 0$, $\left(\frac{x}{y}\right)^n = \frac{x^n}{y^n}$. - For any $a \neq 0$, $\left(a^m\right)^n = a^{mn}$. - Negative exponents mean reciprocal: $a^{-n} = \frac{1}{a^n}$. 3. **Apply the negative exponent:** $$\left(\frac{2^{\frac{1}{4}}}{14^{\frac{1}{4}}}\right)^{-3} = \left(\frac{14^{\frac{1}{4}}}{2^{\frac{1}{4}}}\right)^3$$ 4. **Rewrite the expression inside the parentheses:** $$\left(\frac{14}{2}\right)^{\frac{1}{4} \times 3} = 7^{\frac{3}{4}}$$ 5. **Final simplified form:** $$7^{\frac{3}{4}}$$ This is the simplified expression.