Question

An expression was simplified to 24^12
. 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 apply the Product Rule of Exponents, we use the rule that states \( a^m \cdot a^n = a^{m+n} \).

Given the expression \( 24^{12} \), we need to find how it can be written in a form that exemplifies the Product Rule.

Let's analyze the options provided:

1. **\( 12^4 \times 12^8 \)**: This simplifies to \( 12^{(4 + 8)} = 12^{12} \), which is not \( 24^{12} \).

2. **\( 6^4 \times 4^3 \)**: This does not simplify to \( 24^{12} \) since \( 6 \) and \( 4 \) are not the same base.

3. **\( 24^4 \times 24^8 \)**: This simplifies to \( 24^{(4 + 8)} = 24^{12} \). This is the correct expression to show \( 24^{12} \).

4. **\( 24^3 \times 24^4 \)**: This simplifies to \( 24^{(3 + 4)} = 24^{7} \), which is not \( 24^{12} \).

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

**\( 24^4 \times 24^8 \)**.