Solving a 'Harvard' University entrance exam question

To solve exponential expressions like 64³ - 32³, convert numbers to the same base (64 = 2⁶, 32 = 2⁵), apply the power of a power property (a^(m×n) = (a^m)^n) to get 2¹⁸ - 2¹⁵, factor out the common term 2¹⁵ to obtain 2¹⁵ × (2³ - 1) = 2¹⁵ × 7, then calculate the final value as 229,376.