To simplify the expression \( m^2 \sqrt{m^{10}} \):

1. Start by simplifying the square root. 
   \[
   \sqrt{m^{10}} = m^{10/2} = m^5
   \]
   
2. Now, substitute this back into the expression:
   \[
   m^2 \times m^5
   \]
   
3. Combine the exponents, since the bases are the same (use the rule \( a^m \times a^n = a^{m+n} \)):
   \[
   m^{2+5} = m^7
   \]

So, \( m^2 \sqrt{m^{10}} = m^7 \).

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

Here are five related questions to expand your understanding:

1. How would you simplify \( n^3 \sqrt{n^8} \)?
2. What is the result of \( a^4 \sqrt{a^{6}} \)?
3. How would you simplify \( b^2 \sqrt{b^2} \)?
4. What happens if you have \( c^x \sqrt{c^y} \), and how do you simplify it?
5. How do you express \( m^2 \cdot m^7 \) as a single power?

**Tip:** When simplifying expressions with square roots, always remember that \( \sqrt{a^n} \) can be written as \( a^{n/2} \).

Learn how to simplify the expression m^2√m^10 by applying the rules of exponents and simplifying radicals. This step-by-step solution is ideal for students in Grades 9-10 looking to strengthen their algebra skills.

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