Find the value of
`((1)/(2))^(-2) + ((1)/(3))^(-2) + ((1)/(4))^(-2)`

Answer

To solve the expression \(\left(\frac{1}{2}\right)^{-2} + \left(\frac{1}{3}\right)^{-2} + \left(\frac{1}{4}\right)^{-2}\), we will use the property of exponents that states \(a^{-m} = \frac{1}{a^m}\) or equivalently \(\left(\frac{a}{b}\right)^{-m} = \left(\frac{b}{a}\right)^{m}\).

### Step-by-step Solution:

1. **Rewrite each term using the property of negative exponents**:
\[ \left(\frac{1}{2}\right)^{-2} = 2^2 \]
\[ \left(\frac{1}{3}\right)^{-2} = 3^2 \]
\[ \left(\frac{1}{4}\right)^{-2} = 4^2 \]

2. **Calculate each exponent**:
\[ 2^2 = 4 \]
\[ 3^2 = 9 \]
\[ 4^2 = 16 \]

3. **Add the results together**:
\[ 4 + 9 + 16 \]

4. **Perform the addition**:
\[ 4 + 9 = 13 \]
\[ 13 + 16 = 29 \]

5. **Final Result**:
\[ \left(\frac{1}{2}\right)^{-2} + \left(\frac{1}{3}\right)^{-2} + \left(\frac{1}{4}\right)^{-2} = 29 \]