Step-by-step Solution:

To find the real number in the expansion of \( 4^{2.5} \): 1. Rewrite 4 as a power of 2: \[ 4 = 2^2 \] So, \[ 4^{2.5} = (2^2)^{2.5} \] 2. Use the exponent rule \((a^m)^n = a^{m \cdot n}\): \[ (2^2)^{2.5} = 2^{2 \times 2.5} = 2^5 \] 3. Calculate \( 2^5 \): \[ 2^5 = 32 \] Thus, the real number is 32.