Question

An expression was simplified to 2412
. Which expression correctly used the Product Rule of Exponents to simplify? (1 point)
Responses

124⋅128
12 superscript 4 baseline times 12 superscript 8 baseline

244⋅248
24 superscript 4 baseline times 24 superscript 8 baseline

64⋅43
6 superscript 4 baseline times 4 cubed

243⋅244

Answer 1

To determine which expression correctly simplifies to 2412 using the Product Rule of Exponents, we need to recall the Product Rule of Exponents states that when multiplying two expressions with the same base, you add their exponents:

\[
a^m \cdot a^n = a^{m+n}
\]

Let's analyze each of the options provided:

1. **124 · 128**
- This can be rewritten as \(12^4 \cdot 12^8\).
- Using the Product Rule: \(12^{4 + 8} = 12^{12}\). **(Not equal to 2412)**

2. **244 · 248**
- This can be rewritten as \(24^4 \cdot 24^8\).
- Using the Product Rule: \(24^{4 + 8} = 24^{12}\). **(Not equal to 2412)**

3. **64 · 43**
- This can be rewritten as \(6^4 \cdot 4^3\).
- The bases are different, so this does not apply the Product Rule. **(Not equal to 2412)**

4. **243 · 244**
- This can be rewritten as \(24^3 \cdot 24^4\).
- Using the Product Rule: \(24^{3 + 4} = 24^7\). **(Not equal to 2412)**

Since none of the options provided actually led to the result of \(2412\), it may be necessary to review the problem. The expression given in \(2412\) doesn't seem to correlate with any of the provided choices using the Product Rule of Exponents.

If \(2412\) is meant to be interpreted differently, such as \(12^{12}\) or \(24^{12}\) based on common misinterpretation, please clarify or check again for clarity.

The correct expressions based on initial inputs do not yield \(2412\) accurately under the provided operations.