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The expression you provided is:

\[
\sqrt[8]{x^{16} y^8}
\]

Let's simplify this step-by-step.

1. The 8th root of a power can be simplified using the rule: \(\sqrt[n]{a^m} = a^{m/n}\).

2. Applying this rule to each part of the expression:

\[
\sqrt[8]{x^{16}} = x^{16/8} = x^2
\]
\[
\sqrt[8]{y^8} = y^{8/8} = y^1 = y
\]

3. Thus, the simplified expression becomes:

\[
x^2 y
\]

Would you like further details on how this works?

Here are 5 related questions to explore this further:

1. How do fractional exponents relate to radicals?
2. What is the general rule for simplifying expressions with different roots?
3. Can you simplify expressions with variables raised to negative exponents?
4. How would you simplify a cube root, like \(\sqrt[3]{x^9}\)?
5. What happens when the exponent inside the radical is smaller than the index of the root?

**Tip:** When dealing with roots and exponents, always look for opportunities to simplify by reducing fractions in the exponent!

Simplify the expression \(\sqrt[8]{x^{16} y^8}\).

Learn how to simplify the radical expression \(\sqrt[8]{x^{16} y^8}\) using the properties of exponents and radicals. This problem demonstrates step-by-step simplification for algebraic expressions with fractional exponents. Suitable for students in Grades 8-10.

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