The value of `(5)/(121^(-(1)/(2)))` is

Options

A. `-55`
B. `(1)/(55)`
C. `-(1)/(55)`
D. 55

Answer

To solve the expression \(\frac{5}{121^{-\frac{1}{2}}}\), we can follow these steps:

### Step 1: Rewrite the expression using the property of negative exponents
The property of exponents states that \(a^{-m} = \frac{1}{a^m}\). Thus, we can rewrite \(121^{-\frac{1}{2}}\) as:
\[ 121^{-\frac{1}{2}} = \frac{1}{121^{\frac{1}{2}}} \]
So, the expression becomes:
\[ \frac{5}{121^{-\frac{1}{2}}} = 5 \cdot 121^{\frac{1}{2}} \]

### Step 2: Simplify \(121^{\frac{1}{2}}\)
Next, we need to evaluate \(121^{\frac{1}{2}}\). The square root of \(121\) is:
\[ 121^{\frac{1}{2}} = \sqrt{121} = 11 \]

### Step 3: Substitute back into the expression
Now we substitute \(11\) back into the expression:
\[ 5 \cdot 121^{\frac{1}{2}} = 5 \cdot 11 \]

### Step 4: Calculate the final value
Now, we multiply \(5\) by \(11\):
\[ 5 \cdot 11 = 55 \]

Thus, the value of \(\frac{5}{121^{-\frac{1}{2}}}\) is \(55\).

### Final Answer
The value is \(55\).

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