An expression was simplified to 24^12

Question

. 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 - no response given

243⋅244
24 cubed times 24 to the 4th power - no response given

64⋅43
6 to the 4th power times 4 cubed - no response given

124⋅128
12 to the 4th power times 12 to the 8th power - incorrect
Remaining Attempts
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Answer 1

The Product Rule of Exponents states that when multiplying two expressions with the same base, you can add the exponents. The general formula is:

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

In the case of the expression \(24^{12}\), we want to find two expressions with the base 24 that add up to 12.

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

2. \(24^3 \cdot 24^4\): Using the Product Rule, \(24^3 \cdot 24^4 = 24^{3+4} = 24^{7}\) — This is incorrect.

3. \(6^4 \cdot 4^3\): This does not involve the base 24, hence it is irrelevant to simplifying \(24^{12}\).

4. \(12^4 \cdot 12^8\): Using the Product Rule, \(12^4 \cdot 12^8 = 12^{4+8} = 12^{12}\) — This is also incorrect since it does not involve 24.

The correct answer that correctly uses the Product Rule of Exponents to simplify to \(24^{12}\) is:

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