Question

An expression was simplified to 24^12. Which expression correctly used the Product Rule of Exponents to simplify? (1 point)
Responses

24^4⋅24^8

6^4⋅4^3

24^3⋅24^4

12^4⋅12^8

Answer 1

To determine which expression correctly uses the Product Rule of Exponents, we need to recall the Product Rule itself: \( a^m \cdot a^n = a^{m+n} \).

We are looking for an expression that, when simplified using this rule, results in \( 24^{12} \).

Let's analyze each option:

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

2. **\( 6^4 \cdot 4^3 \)**:
- This does not have the same base, so it cannot be simplified to \( 24^{12} \) using the Product Rule.

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

4. **\( 12^4 \cdot 12^8 \)**:
- Using the Product Rule: \( 12^4 \cdot 12^8 = 12^{4+8} = 12^{12} \)
- This does not produce \( 24^{12} \), so it is incorrect.

The only expression that simplifies correctly to \( 24^{12} \) using the Product Rule is **\( 24^4 \cdot 24^8 \)**.