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(frac(-3)(2))^(-1)= ?...

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

A

(a) `frac(2)(3)`

B

(b) `frac(-2)(3)`

C

(c) `frac(3)(2)`

D

(d) none of these

Text Solution

AI Generated Solution

The correct Answer is:
To solve the expression \((\frac{-3}{2})^{-1}\), we can follow these steps: ### Step 1: Understand the Negative Exponent The negative exponent indicates that we need to take the reciprocal of the base. In this case, the base is \(\frac{-3}{2}\). ### Step 2: Write the Reciprocal Taking the reciprocal of \(\frac{-3}{2}\) gives us: \[ \frac{-2}{-3} \] ### Step 3: Simplify the Expression When we simplify \(\frac{-2}{-3}\), the negatives cancel out: \[ \frac{-2}{-3} = \frac{2}{3} \] ### Final Answer Thus, the value of \((\frac{-3}{2})^{-1}\) is: \[ \frac{2}{3} \] ---
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