Question

An expression was simplified to 24 superscript 12
. 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

24 superscript 3⋅24 superscript 4

Answer 1

The Product Rule of Exponents states that when multiplying two expressions with the same base, you can add the exponents. The rule can be expressed as:

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

Looking at the options provided, we need to identify which expression correctly uses the Product Rule of Exponents to simplify to \( 24^{12} \).

1. \( 12^4 \cdot 12^8 \) simplifies to \( 12^{4+8} = 12^{12} \) (not applicable to base 24).
2. \( 24^4 \cdot 24^8 \) simplifies to \( 24^{4+8} = 24^{12} \) (correct).
3. \( 6^4 \cdot 4^3 \) does not have the same base and does not simplify to \( 24^{12} \).
4. \( 24^3 \cdot 24^4 \) simplifies to \( 24^{3+4} = 24^7 \) (not equal to \( 24^{12} \)).

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

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