To determine which expression is correctly developed to use the Product Rule of Exponents, we need to clarify what the Product Rule of Exponents states. The Product Rule states that when you multiply two powers that have the same base, you add the exponents. Mathematically, this can be expressed as:
\[ a^m \cdot a^n = a^{m+n} \]
Now let's look at the expressions you've provided:
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62.73: This appears to be a decimal number, not an exponent expression.
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327: This also looks like a whole number and does not represent an exponent expression.
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108 . 108: This is equivalent to \( 108^1 \cdot 108^1 \). Using the Product Rule, this equals \( 108^{1+1} = 108^2 \).
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(52) °: This expression seems incomplete. If you intended it to mean \( (5^2) \), then it's just a singular term, not a multiplication of two like bases.
From the evaluation above, the expression 108 . 108 is the only one that correctly applies the Product Rule of Exponents since it translates to \( 108^1 \cdot 108^1 \) and follows the rule by allowing for adding exponents.
Thus, the correct expression developed to use the Product Rule of Exponents is 108 . 108.
1 answer