To simplify the expression $\sqrt{16c^{19}}$, follow these steps:

1. Separate the square root: Break it down into the product of square roots:

$\sqrt{16c^{19}} = \sqrt{16} \times \sqrt{c^{19}}$

2. Simplify the square root of 16:

$\sqrt{16} = 4$

3. Simplify the square root of $c^{19}$:

$\sqrt{c^{19}} = c^{\frac{19}{2}} = c^9 \times \sqrt{c}$

So, putting it all together:

$\sqrt{16c^{19}} = 4c^9 \times \sqrt{c}$

The simplified expression is:

$4c^9 \sqrt{c}$

Would you like more details or have any questions? Here are some related questions you might find helpful:

1. How do you simplify $\sqrt{25c^{10}}$?
2. What is the simplified form of $\sqrt{9c^{14}}$?
3. How do you simplify expressions with fractional exponents?
4. What is the square root of a negative number?
5. How do you simplify $\sqrt{64c^{20}}$?

Tip: When simplifying square roots with variables, remember to split the exponent into an even part and an odd part to make the simplification easier.