The Product Rule of Exponents states that when you multiply two expressions with the same base, you add their exponents. Based on your question, to identify which expression correctly uses the Product Rule of Exponents, we need to look for pairs of terms with the same base.
Let’s evaluate your options:
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108⋅108: This can be expressed as \(10^8 \times 10^8\), which follows the Product Rule.
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10⁸ × 10⁸: This is a direct application of the Product Rule since both terms have the same base (10); it simplifies to \(10^{8+8}=10^{16}\).
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327 32⁷: These bases (32 and 327) are different. This does not involve the Product Rule.
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(52)⁹ (5²)⁹: This expression has the same base (5) in both terms; however, the exponents are the same (9). This could utilize the Power Rule, but it does not display an application of the Product Rule.
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62⋅73: These bases (6 and 7) are different. This does not involve the Product Rule.
Among these options, both of the first two options (108⋅108 and 10⁸ × 10⁸) correctly utilize the Product Rule of Exponents. Therefore, you have a few correct answers, with the most clear cut being:
10⁸ × 10⁸.