To simplify an expression using the Product Rule of Exponents, you need to remember that the Product Rule states:
\[ a^m \cdot a^n = a^{m+n} \]
where \(a\) is the base and \(m\) and \(n\) are the exponents.
Let's break down the given options to check which correctly applies the Product Rule:
- 100 ⋅ 8: This does not apply the Product Rule.
- 100^7: This is also not an application of the Product Rule as it's just a single expression.
- 100^56: Again, this is not applying the Product Rule.
- 10,000^15: This is also a standalone expression with no application of the rule.
- 200^15: This is another standalone expression.
- 100^15: This is also not applying the rule.
None of the provided expressions seem to show a clear application of the Product Rule where two bases are being multiplied. If you can clarify the exact expressions (e.g., are they meant to be multiplied to another), I can help further! If you're looking for an expression that shows the Product Rule in action, something like \(100^7 \cdot 100^15\) which would simplify to \(100^{7+15} = 100^{22}\) would be an appropriate example.
Please provide the full expressions you're referring to if there's additional context!