Question

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

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

243⋅244
24 cubed times 24 to the 4th power

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

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

Answer 1

To use the Product Rule of Exponents, you add the exponents when multiplying numbers with the same base.

The Product Rule states:
\( a^m \cdot a^n = a^{m+n} \)

Let's evaluate the given options to see which one simplifies to \( 2412 \).

1. **\( 24^4 \cdot 24^8 \)**
Using the Product Rule:
\( 24^4 \cdot 24^8 = 24^{4 + 8} = 24^{12} \)

2. **\( 24^3 \cdot 24^4 \)**
Using the Product Rule:
\( 24^3 \cdot 24^4 = 24^{3 + 4} = 24^7 \)

3. **\( 12^4 \cdot 12^8 \)**
Using the Product Rule:
\( 12^4 \cdot 12^8 = 12^{4 + 8} = 12^{12} \)

4. **\( 6^4 \cdot 4^3 \)**
This expression has different bases, so the Product Rule doesn't directly apply; additional simplification would be needed.

None of the options simplify to \( 24^{12} \) directly, but since none of the options lead to 2412 (assuming it meant \( 24^{12} \)), if \( 2412 \) only refers to an exponent on 12, you'd still need to identify that no expression leads there either.

Looking again at the context:
If \( 2412 \) were meant as \( 24^{12} \), then **the correct choice based on Product Rule** is \( 24^4 \cdot 24^8 \).

That would be your answer: **\( 24^4 \cdot 24^8\)** simplifies correctly by the Product Rule to \( 24^{12} \), which appears to form the context claimed by number 2412 (as exponent-related).