To simplify the expression \((x^3 y^{16})^{1/3}\), we apply the power of a product property, which states:

\[
(a^m b^n)^p = a^{m \cdot p} b^{n \cdot p}
\]

Using this, we can distribute the exponent \( \frac{1}{3} \) to both the \(x^3\) and \(y^{16}\):

\[
(x^3 y^{16})^{1/3} = x^{3 \cdot \frac{1}{3}} \cdot y^{16 \cdot \frac{1}{3}} = x^1 \cdot y^{\frac{16}{3}}
\]

This simplifies to:

\[
x \cdot y^{\frac{16}{3}}
\]

Thus, the simplified expression is:

\[
x \cdot y^{\frac{16}{3}}
\]

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. How would you simplify \((x^5 y^8)^2\)?
2. What is the simplified form of \((a^6 b^{12})^{1/2}\)?
3. How do you simplify expressions with fractional exponents like \( (x^4)^{1/2} \)?
4. What happens if you have negative exponents, like \((x^{-2} y^{3})^{1/3}\)?
5. How would you deal with complex numbers in an expression like this?

**Tip:** When simplifying expressions with exponents, always apply the exponent to every term inside the parentheses.

Learn how to simplify the expression (x^3y^16)^(1/3) by applying the power of a product rule. This solution demonstrates the steps in simplifying algebraic expressions with exponents, covering concepts such as distributing exponents. Ideal for students in Grades 9-10.

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