1. Let's understand the problem: Why use $2^6$ instead of $4^3$? 2. Both expressions represent powers and can be compared by expressing them with the same base. 3. Recall that $4 = 2^2$, so $4^3 = (2^2)^3$. 4. Using the power of a power rule: $ (a^m)^n = a^{m \times n} $, we get $$4^3 = (2^2)^3 = 2^{2 \times 3} = 2^6$$ 5. Therefore, $2^6$ and $4^3$ are actually equal because they represent the same number. 6. The choice to use $2^6$ instead of $4^3$ depends on the context or which base is more convenient for the problem. 7. In summary, $2^6 = 4^3 = 64$. This shows that both expressions are equivalent, just written with different bases.