Answer
$49a^{4}b^{10}c^{2}$
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, $(-7a^{2}b^{5}c)^{2}=(-7)^{2}\times (a^{2})^{2}\times (b^{5})^{2}\times c^{2}=49\times (a^{2})^{2}\times (b^{5})^{2}\times c^{2}$.
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, $49\times (a^{2})^{2}\times (b^{5})^{2}\times c^{2}=49\times a^{2\times2}\times b^{5\times2}\times c^{2}=49a^{4}b^{10}c^{2}$.
