Compare 4³ and 8². Which statement is correct?

Compare $4^{3}$ and $8^{2}$ . Which statement is correct?

Class 8Cubes and Cube RootsCubes and Roots

4^{3} = 64

and

8^{2} = 64

, so the two are equal. It is a useful reminder that a cube is not automatically larger than a square — the base matters as much as the power.

Answer: D)

4^{3} = 8^{2}

Both are repeated multiplication, but with key differences:

- A square is non-negative:

(- 5)^{2} = + 25

.
- A cube **keeps the sign**:

(- 5)^{3} = - 125

. (Three negatives stay odd → still negative.)
- Squares grow more slowly than cubes:

5^{2} = 25

5^{3} = 125. -

For square roots, only positive results (by convention). For cube roots, the sign matches the input: ∛

(- 27) = - 3

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