Which expression is correctly developed to use the Product Rule of

To correctly apply the Product Rule of Exponents, we use the property that states \( a^m \cdot a^n = a^{m+n} \), where the bases are the same.

Let's examine the given expression step by step.

The expression you provided is a bit unclear due to the formatting, but it seems like you might be trying to represent the multiplication of several exponential terms.

Let’s break down the expression as you wrote it and assume it's a multiplication of various exponentials:

1. First, we need to identify terms with the same bases and then use the Product Rule of Exponents to combine them.
2. The expression has a form that looks like it might be \( 5^2 \cdot 2^7 \cdot 3^{10} \cdot 8^{10} \).

For instance, if you have something like \( 2^3 \cdot 2^4 \), according to the Product Rule,
- You would combine these as \( 2^{3+4} = 2^7 \).

If the bases differ, the Product Rule of Exponents would not apply directly (e.g., \( 2^3 \cdot 3^4 \) cannot be simplified together in this context).

Please confirm the specific expression to analyze, or provide more information to clarify your question so I can assist you better!