How to Simplify (49s^8)^(1/2) - Easy Explanation for 11-Year-Old Students

Let's simplify the expression (49s⁸)^{1/2} step by step:

1. Understand the expression: The expression means we're taking the square root (because of the exponent 1/2) of the whole quantity inside the parentheses: 49 times s to the eighth power.
2. Split the expression: We can write it as:
   (49)^{1/2} × (s^{8})^{1/2}
3. Simplify each part:
   - The square root of 49 is 7, because 7 × 7 = 49.
   - For the variable, when you raise a power to another power, you multiply the exponents: (s^{8})^{1/2} = s^{8 × (1/2)} = s^{4}.
4. Put it all together:
   So, (49s^{8})^{1/2} = 7 × s^{4} = 7s⁴.

Final answer: 7s⁴