If \( x^{3}=-27 \), then what is \( x \) ? \( 0^{-9} \) \( 0^{-3} \)

Solve the equation by following steps: - step0: Solve for \(x\): \(x^{3}=-27\) - step1: Simplify the equation: \(\sqrt[3]{x^{3}}=\sqrt[3]{-27}\) - step2: Calculate: \(x=\sqrt[3]{-27}\) - step3: Simplify the root: \(x=-3\) Let's solve the problem step by step. 1. **Finding \( x \) from the equation \( x^{3} = -27 \)**: - To solve for \( x \), we take the cube root of both sides: \[ x = \sqrt[3]{-27} \] - The cube root of \(-27\) is \(-3\). Therefore, we have: \[ x = -3 \] 2. **Calculating \( 0^{-9} \)**: - The expression \( 0^{-9} \) represents \( \frac{1}{0^{9}} \). Since \( 0^{9} = 0 \), this results in division by zero, which is undefined. 3. **Calculating \( 0^{-3} \)**: - Similarly, \( 0^{-3} \) represents \( \frac{1}{0^{3}} \). Again, since \( 0^{3} = 0 \), this also results in division by zero, which is undefined. ### Summary of Results: - The value of \( x \) is \( -3 \). - Both \( 0^{-9} \) and \( 0^{-3} \) are undefined due to division by zero.