Calculate the value of $$ a^{-2}b^{4} $$ when $$ a = 2 $$ and $$ b = 3 $$.

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To calculate the value of $$ a^{-2}b^{4} $$ when $$ a = 2 $$ and $$ b = 3 $$, follow these steps:

1. **Substitute the given values into the expression:**
   
   $$
   a^{-2}b^{4} = (2)^{-2} \times (3)^{4}
   $$

2. **Evaluate each part of the expression:**
   
   - **Calculate $$ 2^{-2} $$:**
     
     A negative exponent indicates the reciprocal of the base raised to the positive exponent.
     
     $$
     2^{-2} = \frac{1}{2^{2}} = \frac{1}{4}
     $$
   
   - **Calculate $$ 3^{4} $$:**
     
     $$
     3^{4} = 3 \times 3 \times 3 \times 3 = 81
     $$

3. **Multiply the results:**
   
   $$
   \frac{1}{4} \times 81 = \frac{81}{4} = 20.25
   $$

**Final Answer:**

$$
a^{-2}b^{4} = \frac{81}{4} \quad \text{or} \quad 20.25
$$
$$ a^{-2}b^{4} = \frac{81}{4} $$ or 20.25

Calculate the value of \( a^{-2}b^{4} \) when \( a = 2 \) and \( b = 3 \).

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