Answer
$16a^{16b}$
Work Step by Step
Based on the power of a product rule, we know that $(ab)^{n}=a^{n}b^{n}$ (where $n$ is a positive integer and $a$ and $b$ are real numbers).
Therefore, $(2a^{4b})^{4}=2^{4}\times (a^{4b})^{4}=16\times (a^{4b})^{4}$.
Based on the power rule for exponents, we know that $(a^{m})^{n}=a^{mn}$ (where $m$ and $n$ are positive integers and $a$ is a real number).
Therefore, $16\times (a^{4b})^{4}=16\times a^{4b\times4}=16a^{16b}$.
