Question

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

64⋅43
6 superscript 4 baseline times 4 cubed

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

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

243⋅244

Answer 1

To determine which expression correctly uses the Product Rule of Exponents to simplify to 2412, we need to apply the product rule. The product rule states that when multiplying two powers with the same base, you add the exponents:

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

Now, let's evaluate each response to see which one simplifies to \(24^{12}\).

1. **\(64 \cdot 43\)**:
- This is \(4^3 \cdot 4^3 = 4^{3+3} = 4^6\).

2. **\(124 \cdot 128\)**:
- This is \(12^4 \cdot 12^8 = 12^{4+8} = 12^{12}\).

3. **\(244 \cdot 248\)**:
- This is \(24^4 \cdot 24^8 = 24^{4+8} = 24^{12}\).

4. **\(243 \cdot 244\)**:
- This is \(24^3 \cdot 24^4 = 24^{3+4} = 24^7\).

From the evaluations, the expression that correctly used the Product Rule of Exponents to simplify to \(24^{12}\) is:

**\(244 \cdot 248\) (which is \(24^4 \cdot 24^8\))**.