Evaluate the expression
$$\frac{(1024{)}^{\frac{n}{5}}\times 4^{2n+1}}{16^n\times 4^{n-1}}$$

Let's convert all terms to base 4:
* $1024=4^5⟹(1024{)}^{\frac{n}{5}}=(4^5{)}^{\frac{n}{5}}=4^n$
* $16^n=(4^2{)}^n=4^{2n}$

Substitute these back into the expression:

$$\text{Expression}=\frac{4^n\times 4^{2n+1}}{4^{2n}\times 4^{n-1}}$$

Combine exponents in the numerator and denominator:

$$\text{Numerator}=4^{n+2n+1}=4^{3n+1}$$

$$\text{Denominator}=4^{2n+n-1}=4^{3n-1}$$

Now, divide the values:

$$\text{Expression}=4^{(3n+1)-(3n-1)}=4^2=16$$