`(5^(-1) xx 3^(-1))^(-1)=` ?

Options

A. `frac(1)(15)`
B. `frac(-1)(15)`
C. `15`
D. ` -15 `

Answer

To solve the expression \((5^{-1} \times 3^{-1})^{-1}\), we will follow these steps:

### Step 1: Rewrite the expression
The original expression is:
\[ (5^{-1} \times 3^{-1})^{-1} \]

### Step 2: Apply the property of negative exponents
According to the property of negative exponents, \(a^{-n} = \frac{1}{a^n}\). Therefore, we can rewrite the expression as:
\[ \frac{1}{(5^{-1} \times 3^{-1})} \]

### Step 3: Simplify the expression inside the parentheses
Now, we can simplify \(5^{-1}\) and \(3^{-1}\):
\[ 5^{-1} = \frac{1}{5} \quad \text{and} \quad 3^{-1} = \frac{1}{3} \]
Thus, we have:
\[ (5^{-1} \times 3^{-1}) = \left(\frac{1}{5} \times \frac{1}{3}\right) = \frac{1}{15} \]

### Step 4: Substitute back into the expression
Now substitute \(\frac{1}{15}\) back into the expression:
\[ \frac{1}{(5^{-1} \times 3^{-1})} = \frac{1}{\frac{1}{15}} = 15 \]

### Final Answer
Thus, the final answer is:
\[ 15 \]