1. The problem asks us to classify each expression as either "Equivalent to a natural number" or "Not equivalent to a natural number." A natural number is a positive integer starting from 1, 2, 3, and so on. 2. The expressions given are: - $4^3$ - $(-2)^3$ - $\sqrt[3]{-8}$ - $(-5)^2$ 3. We already know $4^3 = 64$, which is a natural number. 4. Calculate $(-2)^3$: $$(-2)^3 = (-2) \times (-2) \times (-2) = 4 \times (-2) = -8$$ Since $-8$ is negative, it is not a natural number. 5. Calculate $\sqrt[3]{-8}$ (the cube root of $-8$): $$\sqrt[3]{-8} = -2$$ Because $-2$ is negative, it is not a natural number. 6. Calculate $(-5)^2$: $$(-5)^2 = (-5) \times (-5) = 25$$ Since $25$ is positive, it is a natural number. 7. Final classification: - Equivalent to a natural number: $4^3 = 64$, $(-5)^2 = 25$ - Not equivalent to a natural number: $(-2)^3 = -8$, $\sqrt[3]{-8} = -2$ Therefore, the expressions $4^3$ and $(-5)^2$ go in the "Equivalent to a natural number" column, and $(-2)^3$ and $\sqrt[3]{-8}$ go in the "Not equivalent to a natural number" column.