Simplify 2016 and 2015 factorial!

Relevant wiki: Factorials Problem Solving - Basic

$\large\dfrac{2016^{2016}}{\underbrace{2016!\times2016!\times2016!\times\cdots\times2016!}_{2016 \text{ times}}}\underbrace{\times2015!\times2015!\times2015!\times\cdots\times2015!}_{2016 \text{ times}}$

If we imply $\large\ 2016!\implies2015!\times2016$ So that the expression becomes: $\large\implies\dfrac{2016^{2016}}{\underbrace{2015!\times2015!\times2015!\times\cdots\times2015!\times2015!}_{2016 \text{ times}}\times\underbrace{2016\times2016\times2016\times\cdots\times2016\times2016}_{2016 \text{ times}}}\underbrace{\times2015!\times2015!\times2015!\times\cdots\times2015!}_{2016 \text{ times}}$

Now we can eliminate: $\boxed{2015! }$ finally, we can get a simplest expression: $\large\implies\dfrac{2016^{2016}}{\underbrace{2016\times2016\times2016\times\cdots\times2016}_{2016 \text{ times}}} =\dfrac{2016^{2016}}{2016^{2016}} =\boxed{1}$

Relevant wiki: Factorials Problem Solving - Basic

$\Rightarrow \dfrac{\color{#D61F06}{2016^{2016}}}{\underbrace{2016!\times2016!\times2016!\times\cdots\times2016!}_{2016 \text{ times}}}\times\underbrace{\color{#3D99F6}{2015!\times2015!\times2015!\times\cdots\times2015!}}_{2016 \text{ times}}$

$\implies\dfrac{\color{#D61F06}{2016^{2016}}}{\color{#D61F06}{2016^{2016}}×\color{#3D99F6}{2015!^{2016}}}×\color{#3D99F6}{2015!^{2016}}=\color{#69047E}{\boxed{1}}$