Final answer:
The cube root of 729 is 9, therefore both 9 and -9 are solutions to the equation y³ = 729. Numbers 27 and 729 are not solutions.
Step-by-step explanation:
The question asks which of these expressions represent solutions to the equation y³ = 729. To find solutions for this equation, you would take the cube root of 729. The cube root of 729 is 9 because 9³ (9 x 9 x 9) equals 729. Therefore, 9 is a solution to the equation. The negative cube root is also a solution because (-9)³ = -9 x -9 x -9 which also equals 729. Hence, both 9 and -9 are correct. Numbers 27 and 729 are not cube roots of 729, so they do not represent solutions to the equation.
Here are the correct solutions to the equation y³ = 729: