Answer
$64z^{10}$
Work Step by Step
We are given that the square has sides of length $8z^{5}$ decimeters. We know that the area of a square is calculated as $area=length^{2}$.
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, $area=(8z^{5})^{2}=8^{2}(z^{5})^{2}=64(z^{5})^{2}$.
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, $area=64(z^{5})^{2}=64z^{5\times2}=64z^{10}$.