Factorial Fraction

$\large \dfrac{\color{#3D99F6}{10!}^\color{#D61F06}{2}}{\color{#20A900}{9!}^\color{#D61F06}{2}}= \left(\dfrac{\color{#3D99F6}{10!}}{\color{#20A900}{9!}}\right)^\color{#D61F06}{2}=\left(\dfrac{\color{#3D99F6}{9!\times10}}{\color{#20A900}{9!}}\right)^\color{#D61F06}{2}=\color{#3D99F6}{10}^\color{#D61F06}{2}=\color{#D61F06}{\boxed{100}}$

$\Large\dfrac{10!^2}{9!^2}=\dfrac{10!}{9!} \times \dfrac{10!}{9!} = \dfrac{9! \times 10}{9!} \times \dfrac{9! \times 10}{9!}= 10\times 10 = \boxed{100}$

$\begin{aligned} & \dfrac {{10!}^2}{{9!}^2}\\ = & \dfrac {10×9×8×7×6×5×4×3×2×1×10×9×8×7×6×5×4×3×2×1}{9×8×7×6×5×4×3×2×1×9×8×7×6×5×4×3×2×1}\\ = & {\dfrac {10 × \cancel {9×8×7×6×5×4×3×2×1} × 10 × \cancel{9×8×7×6×5×4×3×2×1}}{\cancel {9×8×7×6×5×4×3×2×1} × \cancel{9×8×7×6×5×4×3×2×1}}}\\ = & 10 × 10\\ = & \boxed {100} \end{aligned}$

(10!)2/(9!)2=(10)2×(9!)2/(9!)2 (10)2=100