Answer
$8a^{15}$
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, $(2a^{5})^{3}=2^{3}\times (a^{5})^{3}=8(a^{5})^{3}$.
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, $8(a^{5})^{3}=8a^{5\times3}=8a^{15}$.