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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.

Which expression has the same meaning as \(\sqrt{m^{16}}\)?

Learn how to simplify the square root of \(m^{16}\) using exponent rules. This problem covers key concepts in simplifying expressions with exponents, suitable for Grade 8 students. Step-by-step solution provided.

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