To simplify the expression using the Product Rule of Exponents, we need to remember that when multiplying two expressions with the same base, we add the exponents. The Product Rule states:
\[ a^m \cdot a^n = a^{m+n}. \]
Looking at the options provided, it seems like you've written them in a format that is not entirely clear (likely due to formatting), but let's break down a possible interpretation.
Assuming the base is 100 and we have different exponents combined with the multiplication, we want to ensure that the expressions correctly apply the Product Rule. Here's how it would work:
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If we had an expression like \(100^a \cdot 100^b\), using the Product Rule, we would combine it to \(100^{(a+b)}\).
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If there are multiple terms like \(100^1 \cdot 100^7 \cdot 100^{56} \cdot 100^{15} \cdot 100^{2}\), we would first add the exponents: \(1 + 7 + 56 + 15 + 2\) and then write it as \(100^{(total\ sum)}\).
Without seeing the correct context or formatting for your choices, it’s difficult to specify which option correctly applies the Product Rule.
Please reformat or clarify your options for more precise assistance!
1 answer