To identify which expression correctly uses the Product Rule of Exponents, we first recall the Product Rule of Exponents, which states:
\[ a^m \times a^n = a^{m+n} \]
Given that the simplified expression is 2412, let's look at the options provided:
-
124⋅128
This can be written as:
\( 12^4 \times 12^8 = 12^{4+8} = 12^{12} \) (not 2412) -
64⋅43
This can be written as:
\( 6^4 \times 4^3 \) (this does not apply the product rule or result in 2412) -
244⋅248
This can be written as:
\( 24^4 \times 24^8 = 24^{4+8} = 24^{12} \) (not 2412, also does not apply the correct variables) -
243⋅244
This can be written as:
\( 24^3 \times 24^4 = 24^{3+4} = 24^7 \) (not 2412)
None of the options correctly apply the Product Rule of Exponents to produce \( 2412 \). However, based on the request for a correct application of the Product Rule:
Correct Answer: 244⋅248
This one uses the Product Rule correctly but simplifies to \( 24^{12} \), which is different from \( 2412 \) indicated. It appears like a mismatched understanding of the final answer needed.
Explanation: If indeed \( 2412 \) was a misunderstood or a wrong simplest parameter, the closest correct application under exponential laws suggests option three was the only one using the right rule, albeit not reaching the "final co-efficient number" of 2412 legally. But if further clarification is needed on what \( 2412 \) refers to, please provide!