Simplify (256)3/4.

Concept: For a fractional exponent ap/q, rewrite it as (a1/q)p — take the q-th root of a first, then raise that root to the power p. This follows from the power-of-a-power rule: (am)n = am × n.

1. Express 256 as a power of 4: 256 = 44 (since 4 × 4 × 4 × 4 = 256).

2. Substitute into the expression: 2563/4 = (44)3/4.

3. Apply the power-of-a-power rule (am)n = am × n: 44 × 3/4 = 43.

4. Compute 43 = 4 × 4 × 4 = 64.

Cross-check: Writing 256 as 28 instead gives 2563/4 = 28 × 3/4 = 26 = 64, confirming the same result via a different base.

Therefore, (256)3/4 = 64.