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

To solve the expression \( 4 \times (8^{4})^{2} \), we first simplify \( (8^{4})^{2} \). According to the power of a power property in exponents, we multiply the exponents: \( 8^{4 \times 2} = 8^{8} \). Now, we have \( 4 \times 8^{8} \). Since \( 4 \) can be expressed as \( 2^{2} \), we can rewrite it as \( 2^{2} \times 8^{8} \). Now, recognizing that \( 8 = 2^{3} \), we get \( 8^{8} = (2^{3})^{8} = 2^{24} \). So, we rewrite \( 4 \times 8^{8} \) as \( 2^{2} \times 2^{24} = 2^{26} \). If we want to express \( 2^{26} \) back in terms of powers of \( 8 \), we divide 26 by 3 (since \( 8 = 2^{3} \)) giving us \( 2^{24} \times 2^{2} = 8^{8} \times 4 \). Ultimately, in terms of \( 8 \), it's clear that \( 4 \times (8^{4})^{2} = 8^{8} \). So the answer is **C \( 8^{8} \)**.