Simplify

$\left(2x+10\right)^4\left(x+5\right)^4=\left(\left(2x+10\right)\left(x+5\right)\right)^4$

$\left(\left(2x+10\right)\left(x+5\right)\right)^4=\left(2x+10\right)^4\left(x+5\right)^4$

$\left(2x+10\right)^4\left(x+5\right)^4$ is your answer

$(2x+10)^4(x+5)^4$

$(2(x+5))^4(x+5)^4$

$16(x+5)^4(x+5)^4$

$\color{brown}\boxed{16(x+5)^8}$