simplify the expression $(-5r^{4}s^{10})^{4}$.

Explanation:

Step1: Apply power - of - a - product rule

$(-5r^{4}s^{10})^{4}=(-5)^{4}(r^{4})^{4}(s^{10})^{4}$

Step2: Calculate $(-5)^{4}$

$(-5)^{4}=(-5)\times(-5)\times(-5)\times(-5) = 625$

Step3: Apply power - of - a - power rule for $r$ and $s$ terms

$(r^{4})^{4}=r^{4\times4}=r^{16}$ and $(s^{10})^{4}=s^{10\times4}=s^{40}$

Step4: Combine results

$(-5)^{4}(r^{4})^{4}(s^{10})^{4}=625r^{16}s^{40}$

Answer:

$625r^{16}s^{40}$