\( 4 \times\left(8^{4}\right)^{2}= \) \( 4 \times \quad \) A \( 8^{2} \) \( 4 \times \quad \) B \( 8^{6} \) \( 4 \times \quad \) C \( 8^{8} \) \( 4 \times \quad \) D \( 8^{16} \)

Let's simplify the expression step-by-step. The expression is \( 4 \times (8^4)^2 \). First, using the power of a power property \((a^m)^n = a^{m \cdot n}\), we can simplify \((8^4)^2\) to \(8^{4 \cdot 2} = 8^8\). Now, substituting this back into the original expression gives us: \[ 4 \times 8^8. \] Now looking at the choices provided, we see: - A \( 8^{2} \) - B \( 8^{6} \) - C \( 8^{8} \) - D \( 8^{16} \) Clearly, we have \( 4 \times 8^8\) which doesn't change the base of 8, so while we can't combine those terms like exponents, we see that \( 8^8\) is one of the choices provided. Thus, the answer is: **C \( 8^{8} \)**.