Answer
$x^{10}y^{15}$
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, $(x^{2}y^{3})^{5}=(x^{2})^{5}\times (y^{3})^{5}$.
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, $(x^{2})^{5}\times (y^{3})^{5}=x^{2\times5}\times y^{3\times5}=x^{10}y^{15}$.