5. If \( x^{-3}=27, x= \) (A) -3 (B) \( -\frac{1}{3} \) (C) \( \frac{1}{3} \) (D) 3 (E) 9

To solve the equation \( x^{-3} = 27 \), we can follow these steps: 1. **Rewrite the equation**: The expression \( x^{-3} \) can be rewritten as \( \frac{1}{x^3} \). Therefore, we have: \[ \frac{1}{x^3} = 27 \] 2. **Cross-multiply**: To eliminate the fraction, we can cross-multiply: \[ 1 = 27x^3 \] 3. **Isolate \( x^3 \)**: Now, we can solve for \( x^3 \) by dividing both sides by 27: \[ x^3 = \frac{1}{27} \] 4. **Take the cube root**: To find \( x \), we take the cube root of both sides: \[ x = \sqrt[3]{\frac{1}{27}} \] 5. **Calculate the cube root**: The cube root of \( \frac{1}{27} \) is \( \frac{1}{3} \) because \( \left(\frac{1}{3}\right)^3 = \frac{1}{27} \). Thus, the solution is: \[ x = \frac{1}{3} \] The correct answer is (C) \( \frac{1}{3} \).