1. The problem is to understand cubes and cube roots. 2. The cube of a number $x$ is given by the formula $$x^3 = x \times x \times x$$ which means multiplying the number by itself three times. 3. The cube root of a number $y$ is the number $x$ such that $$x^3 = y$$. It is denoted as $$\sqrt[3]{y}$$. 4. For example, if we want to find the cube of 2, we calculate $$2^3 = 2 \times 2 \times 2 = 8$$. 5. To find the cube root of 27, we look for a number $x$ such that $$x^3 = 27$$. Since $$3^3 = 27$$, the cube root of 27 is 3. 6. Important rules: - Cubing a positive or negative number preserves the sign (e.g., $$(-2)^3 = -8$$). - Cube roots can be taken of negative numbers as well (e.g., $$\sqrt[3]{-8} = -2$$). 7. Summary: Cubing means multiplying a number by itself three times, and the cube root is the inverse operation that finds the original number whose cube is given.