`(frac(1)(2))^(-2)+(frac(1)(3))^(-2)+(frac(1)(4))^(-2)=`?

Options

A. `frac(61)(144)`
B. `29`
C. `frac(144)(61)`
D. none of these

Answer

To solve the expression \((\frac{1}{2})^{-2} + (\frac{1}{3})^{-2} + (\frac{1}{4})^{-2}\), we will follow these steps:

### Step 1: Apply the property of negative exponents
The property of negative exponents states that \(a^{-n} = \frac{1}{a^n}\). Therefore, we can rewrite each term:

\[ (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = 2^2 \]

\[ (\frac{1}{3})^{-2} = \frac{1}{(\frac{1}{3})^2} = 3^2 \]

\[ (\frac{1}{4})^{-2} = \frac{1}{(\frac{1}{4})^2} = 4^2 \]

### Step 2: Calculate the squares
Now we calculate the squares of 2, 3, and 4:

\[ 2^2 = 4 \]

\[ 3^2 = 9 \]

\[ 4^2 = 16 \]

### Step 3: Add the results
Now we add the results from Step 2 together:

\[ 4 + 9 + 16 \]

Calculating this gives:

\[ 4 + 9 = 13 \]
\[ 13 + 16 = 29 \]

### Final Answer
Thus, the final result of the expression \((\frac{1}{2})^{-2} + (\frac{1}{3})^{-2} + (\frac{1}{4})^{-2}\) is:

\[ \boxed{29} \]

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