The Product Rule of Exponents states that when multiplying two powers with the same base, you can add the exponents. This is expressed as:
\[ a^m \cdot a^n = a^{m+n} \]
Let's analyze the given choices to see which one correctly applies the Product Rule of Exponents:
1. **10 to the power of 8 ⋅ 10 to the power of 8**:
- This can be simplified using the Product Rule:
\[ 10^8 \cdot 10^8 = 10^{8+8} = 10^{16} \]
- This correctly applies the Product Rule.
2. **32 to the power of 7**:
- This does not involve multiplication of two powers; it is just a single term.
3. **6 to the power of 2 ⋅ 73**:
- Here, 73 is not a power of 6, which means no Product Rule can be applied.
4. **(5 to the power of 2) times 9**:
- This expression involves 9, which is not a power of 5. Hence, the Product Rule cannot be applied in this case.
Thus, the only expression that correctly uses the Product Rule of Exponents is:
**10 to the power of 8 ⋅ 10 to the power of 8.**