[tex]\displaystyle\\
a=\frac{2^{4n}\cdot5^{2n+2}+800^n}{25^{n+1}+50^n} \\\\\\
a=\frac{2^{4n}\cdot5^{2n}\cdot5^2+(16\cdot 50)^n}
{25^{n+1}+50^n} \\\\\\
a=\frac{2^{4n}\cdot5^{2n}\cdot5^2+(16\cdot 50)^n}
{25^{{n+1}}+50^ n}} \\\\\\
a=\frac{2^{4n}\cdot \Big(5^2\Big)^n\cdot 5^2+16^n\cdot 50^n}
{25^{{n+1}}+50^ n}} \\\\\\
a=\frac{2^{4n}\cdot 25^n\cdot 25+16^n\cdot 50^n}
{25^{{n+1}}+50^ n}} \\\\\\
a=\frac{2^{4n}\cdot 25^{n+1}+\Big(2^4\Big)^n\cdot 50^n}
{25^{{n+1}}+50^ n}}
[/tex]
[tex]\displaystyle\\
a=\frac{2^{4n}\cdot 25^{n+1}+2^{4n}\cdot 50^n}{25^{{n+1}}+50^ n}}\\\\\\
a=\frac{2^{4n} ( 25^{n+1}+ 50^n)}{25^{{n+1}}+50^ n}}\\\\\\
a=2^{4n}= 2^{2n\cdot2} = \Big(2^{2n}\Big)^2 = pp[/tex]
