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((-3)/(7))^(-1)=?...

`((-3)/(7))^(-1)=?`

A

`(7)/(3)`

B

`(-7)/(3)`

C

`(3)/(7)`

D

none of these

Text Solution

AI Generated Solution

The correct Answer is:
To solve the expression \((-3/7)^{-1}\), we need to find the inverse of the rational number \(-3/7\). The inverse of a number \(x\) is defined as \(1/x\). Here are the steps to solve the problem: ### Step-by-Step Solution: 1. **Identify the expression**: We start with the expression \((-3/7)^{-1}\). 2. **Apply the definition of inverse**: The inverse of a number \(a\) is given by \(1/a\). Therefore, we can rewrite the expression as: \[ (-3/7)^{-1} = 1/(-3/7) \] 3. **Simplify the expression**: To divide by a fraction, we multiply by its reciprocal. The reciprocal of \(-3/7\) is \(-7/3\). Thus, we have: \[ 1/(-3/7) = 1 \times (-7/3) = -7/3 \] 4. **Final answer**: Therefore, we conclude that: \[ (-3/7)^{-1} = -7/3 \] ### Conclusion: Thus, the value of \((-3/7)^{-1}\) is \(-7/3\).
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