The problem asks: "Which expression has the same meaning as $\sqrt{m^{16}}$?"

To solve this, we need to simplify the square root of $m^{16}$. Using the property of exponents that states:

$\sqrt{a^n} = a^{\frac{n}{2}},$

we can rewrite $\sqrt{m^{16}}$ as:

$m^{\frac{16}{2}} = m^8.$

Thus, the expression equivalent to $\sqrt{m^{16}}$ is $m^8$.

The correct answer is the option $m^8$.

Would you like more details, or do you have any further questions?

Here are some related questions to expand on this topic:

1. How do you simplify $\sqrt{m^4}$?
2. What is the cube root of $m^9$?
3. How do rational exponents relate to roots?
4. How can you simplify $m^{\frac{1}{3}}$?
5. What is the square root of $m^{18}$?

Tip: When taking the root of an expression, you divide the exponent by the value of the root. For example, for a square root, divide the exponent by 2.