Simplify the quotient of powers $\frac{x^6\sqrt{x^2+2x+1}}{\left(x+2\right)^4}$

$\frac{\sqrt{2x^{12} y^{21} z^8}}{40\sqrt{xy\cdot z}}$

$\frac{\left(x^{\frac{1}{5}} y^{\frac{3}{2}}\right)^{10}}{\left(y^{\left(-1\right)\cdot\frac{2}{5}} x^{\frac{2}{3}}\right)^5}$

$\frac{\left(4x^{121\left(-1\right)} y^4 z^8\right)^3}{\left(9x y^3 z^5\right)^4}$

$\frac{\left(-5x^3 y^2\right)^3\left(x y^5\right)^2}{\left(-5x^{-1}\cdot y\right)^{-1}}$

$\frac{\left(x^{\left(-1\right)\cdot\frac{1}{5}} y^{\frac{3}{2}}\right)^{10}}{\left(y^{\left(-1\right)\cdot\frac{2}{5}} x^{\frac{2}{3}}\right)^5}$

$\frac{\left(4x^3\right)^2}{\left(121\left(-1\right) x^5\right)^3}$

$\frac{24\left(x+y\right)^3\left(x-y\right)^2}{30\left(x+y\right)^2\left(x-y\right)^3}$