question\nfully simplify.\n(5x^2y^4)^5

Explanation:

Step1: Apply power - of - a - product rule

Use the rule $(ab)^n=a^n b^n$. Here $a = 5$, $b=x^{2}y^{4}$ and $n = 5$. So, $(5x^{2}y^{4})^{5}=5^{5}(x^{2})^{5}(y^{4})^{5}$.

Step2: Calculate $5^{5}$

$5^{5}=5\times5\times5\times5\times5 = 3125$.

Step3: Apply power - of - a - power rule

Use the rule $(a^{m})^{n}=a^{mn}$. For $(x^{2})^{5}$, we have $x^{2\times5}=x^{10}$, and for $(y^{4})^{5}$, we have $y^{4\times5}=y^{20}$.

Answer:

$3125x^{10}y^{20}$