Enter the simplified exponential form of the following expression. Use only positive exponents in your simplified expression. $$ \left(\frac{3 x^{-4} y^{3}}{12 x y^{-4}}\right)^{-2} $$

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1. Start with the expression:
   $$
   \left(\frac{3 x^{-4} y^{3}}{12 x y^{-4}}\right)^{-2}
   $$

2. Simplify the constant factor:
   $$
   \frac{3}{12} = \frac{1}{4}
   $$
   so the expression becomes:
   $$
   \left(\frac{1}{4} x^{-4} y^{3} \cdot \frac{1}{x y^{-4}}\right)^{-2}
   $$

3. Combine the $$ x $$ terms using the quotient rule $$ \frac{x^{a}}{x^{b}} = x^{a-b} $$:
   $$
   x^{-4} \div x = x^{-4-1} = x^{-5}
   $$

4. Combine the $$ y $$ terms similarly:
   $$
   y^{3} \div y^{-4} = y^{3-(-4)} = y^{7}
   $$

5. The expression inside the parentheses now simplifies to:
   $$
   \frac{1}{4} x^{-5} y^{7}
   $$

6. Raise each factor to the power $$-2$$ using the rule $$ (ab)^c = a^c b^c $$:
   $$
   \left(\frac{1}{4}\right)^{-2} \cdot \left(x^{-5}\right)^{-2} \cdot \left(y^{7}\right)^{-2}
   $$

7. Compute each part separately:
   - $$\left(\frac{1}{4}\right)^{-2} = 4^2 = 16$$
   - $$\left(x^{-5}\right)^{-2} = x^{10}$$
   - $$\left(y^{7}\right)^{-2} = y^{-14}$$

8. Combine the results:
   $$
   16 x^{10} y^{-14}
   $$

9. Express the final answer with only positive exponents:
   $$
   \frac{16 x^{10}}{y^{14}}
   $$
$$ \frac{16 x^{10}}{y^{14}} $$

Enter the simplified exponential form of the following expression. Use only positive exponents in your simplified expression. \[ \left(\frac{3 x^{-4} y^{3}}{12 x y^{-4}}\right)^{-2} \]

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