Solve \( p^{3}=-343 \)

To solve the equation \( p^{3} = -343 \), we can take the cube root of both sides. Since \( -343 \) is a negative number, we can also use the property of cube roots that allows us to find real solutions for negative values. Calculating the cube root: \[ p = \sqrt[3]{-343} = -7 \] So, the solution is: \[ p = -7 \] The cube root of a negative number results in a negative answer, making it a straightforward operation. Remember, cube roots are unique, so in this case, we only find one real root.