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.