Sure! To place $16x^8y^{12}$ under the square root sign, you write it as:

$\sqrt{16x^8y^{12}}$

If you want to simplify the expression further, we can break it down:

1. $\sqrt{16} = 4$
2. $\sqrt{x^8} = x^4$ (since $\sqrt{x^8} = x^{8/2}$)
3. $\sqrt{y^{12}} = y^6$ (since $\sqrt{y^{12}} = y^{12/2}$)

So, simplifying the entire expression gives:

$\sqrt{16x^8y^{12}} = 4x^4y^6$

Let me know if you'd like further clarification or a different approach!

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Here are 5 related questions you can explore next:

1. How do you simplify expressions with cube roots or higher roots?
2. What are the properties of square roots that help in simplifying polynomials?
3. How do you deal with square roots involving variables with fractional exponents?
4. What happens when you have negative exponents inside square roots?
5. How can you solve equations involving square roots?

Tip: When simplifying expressions under a square root, always separate constants, variables, and powers for easier simplification!