To determine which expression is correctly developed to use the Product Rule of Exponents, we need to recall the Product Rule itself, which states that when you multiply two expressions with the same base, you add their exponents.
Let's analyze each expression:
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327: This does not show any exponent rules being applied.
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32 to the 7th power: This shows a base of 3 and an exponent of 2, multiplied by 7, which is somewhat related but not an application of the Product Rule.
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62⋅73: This is the product of two terms with different bases (6 and 7). The Product Rule is not demonstrated here.
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108⋅108: This can be expressed as \(10^8 \cdot 10^8\). According to the Product Rule of Exponents, you would add the exponents: \(10^{8+8} = 10^{16}\). This shows the application of the Product Rule.
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(52)9: This can be rewritten as \(5^2\) raised to the 9th power, which would apply the rule \( (a^m)^n = a^{mn} \), not the Product Rule.
Therefore, the expression that correctly represents the use of the Product Rule of Exponents is:
108⋅108, which simplifies to \(10^{16}\) using the Product Rule.
1 answer