To simplify $(2x^2y)^3$ without using negative exponents, we apply the power of a product rule, which states that $(abc)^n = a^n \cdot b^n \cdot c^n$, and apply the power of a power rule, which states that $(a^m)^n = a^{m \cdot n}$.

Let's break it down step by step:

$(2x^2y)^3 = (2)^3 \cdot (x^2)^3 \cdot (y)^3$

Now, simplify each part:

• $2^3 = 8$
• $(x^2)^3 = x^{2 \cdot 3} = x^6$
• $y^3 = y^3$

Putting it all together:

$(2x^2y)^3 = 8x^6y^3$

So, the simplified expression is:

$8x^6y^3$

Would you like further clarification on any of the steps?

Here are 5 follow-up questions you can explore:

1. How do negative exponents affect the simplification process?
2. Can the power of a product rule be applied to more than three factors?
3. What are some other exponent rules that help with simplifying expressions?
4. How would you simplify an expression like $(3a^2b^3)^4$?
5. How does this simplification work when dealing with fractions or terms in the denominator?

Tip: Always distribute the exponent across each factor in the parentheses when simplifying products raised to a power!