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The given expression is:

\[
\sqrt{49x^{10}}
\]

We need to simplify this. Let's break it down step by step.

### Step 1: Simplify the square root of 49
Since 49 is a perfect square:

\[
\sqrt{49} = 7
\]

### Step 2: Simplify the square root of \( x^{10} \)
The square root of \( x^{10} \) can be written as:

\[
\sqrt{x^{10}} = x^{10/2} = x^5
\]

### Step 3: Combine the results
Putting everything together:

\[
\sqrt{49x^{10}} = 7x^5
\]

Thus, the simplified expression is:

\[
7x^5
\]

Would you like further details or have any questions?

### Related questions:
1. How do you simplify expressions with fractional exponents?
2. What is the general rule for simplifying square roots of powers of variables?
3. How do you simplify cube roots of powers, for example \( \sqrt[3]{x^9} \)?
4. What happens if \( x \) is not a positive real number in this kind of expression?
5. How do you simplify the expression \( \sqrt{a^m b^n} \) when both \( a \) and \( b \) are variables?

**Tip:** When simplifying expressions with square roots and powers, always look for perfect squares to simplify first.

Simplify \( \sqrt{49x^{10}} \), assuming that \( x \) represents a positive real number.

Learn how to simplify the expression \( \sqrt{49x^{10}} \). This problem covers the square root of a product and exponent rules, making it suitable for students in Grades 9-10.

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