Ah, I see! You meant \( 50 \times 14^x \) under the square root. Let's simplify that:

Given expression:
\[
\sqrt{50 \times 14^x}
\]

### Step 1: Apply the square root property.
\[
\sqrt{50 \times 14^x} = \sqrt{50} \times \sqrt{14^x}
\]

### Step 2: Simplify each part.
- \( \sqrt{50} = \sqrt{25 \times 2} = 5 \sqrt{2} \)
- \( \sqrt{14^x} = 14^{x/2} \) (since \( \sqrt{a^b} = a^{b/2} \))

### Final result:
\[
\sqrt{50 \times 14^x} = 5 \sqrt{2} \times 14^{x/2}
\]

Thus, the simplified expression is:
\[
5 \sqrt{2} \times 14^{x/2}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify expressions with exponents under square roots?
2. What are the properties of exponents when multiplying terms?
3. How do you handle mixed constant and variable terms in square roots?
4. Can square roots be simplified further for larger numbers?
5. How do you simplify cube roots compared to square roots?

**Tip:** Remember that \( \sqrt{a^b} = a^{b/2} \), which is useful when simplifying expressions with exponents inside square roots.

Learn how to simplify \( \sqrt{50 \times 14^x} \) step-by-step with detailed explanations. This problem involves using the square root property and handling exponents under square roots effectively. Suitable for students in Grades 9-12.

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