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To simplify the given expression:

\[ \left( \left( \sqrt[17]{w^{14}} \right)^2 \right)^{\frac{17}{14}} \]

we can follow these steps:

1. First, simplify inside the parentheses:
\[ \sqrt[17]{w^{14}} = w^{\frac{14}{17}} \]

2. Raise this result to the power of 2:
\[ \left( w^{\frac{14}{17}} \right)^2 = w^{\frac{14}{17} \cdot 2} = w^{\frac{28}{17}} \]

3. Now, raise this result to the power of \(\frac{17}{14}\):
\[ \left( w^{\frac{28}{17}} \right)^{\frac{17}{14}} = w^{\frac{28}{17} \cdot \frac{17}{14}} = w^2 \]

Therefore, the simplified result is:

\[ w^2 \]

Would you like more details or have any questions?

Here are five related questions:
1. What are the properties of exponents and how are they applied in simplification?
2. How do you simplify expressions involving roots and fractional exponents?
3. Can you explain the process of converting roots to fractional exponents?
4. How does the power of a power property work in exponentiation?
5. What are the common mistakes to avoid when simplifying complex exponent expressions?

**Tip:** When simplifying expressions with multiple exponents and roots, always start by converting roots to fractional exponents for easier manipulation.

Simplify the given expression: ((17√(w^14))^2)^(17/14)

Learn how to simplify the expression ((17√(w^14))^2)^(17/14) using properties of exponents and roots. This problem covers key algebraic concepts suitable for students in Grades 9-12.

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