An expression was simplified to 2412

Question

. Which expression correctly used the Product Rule of Exponents to simplify?(1 point)
Responses

124⋅128
12 to the 4th power times 12 to the 8th power

64⋅43
6 to the 4th power times 4 cubed

244⋅248
24 to the 4th power times 24 to the 8th power

243⋅244

Answer 1

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:

1. 124⋅128
   This can be written as:
   ${12}^4\times {12}^8={12}^{4+8}={12}^{12}$ (not 2412)

2. 64⋅43
   This can be written as:
   $6^4\times 4^3$ (this does not apply the product rule or result in 2412)

3. 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)

4. 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!