simplify to a single power of 4: \\((4^3)^5\\)

Explanation:

Step1: Recall the power of a power rule

The power of a power rule states that ((a^m)^n = a^{m\times n}). Here, (a = 4), (m = 3), and (n = 5).

Step2: Apply the rule

Using the rule ((4^3)^5 = 4^{3\times5}). Calculating (3\times5 = 15), so ((4^3)^5 = 4^{15}).

Answer:

(4^{15}) (The exponent in the box should be 15)