Question
An expression was simplified to 2412
. 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
243⋅244
24 cubed times 24 superscript 4 baseline
64⋅43
. 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
243⋅244
24 cubed times 24 superscript 4 baseline
64⋅43
Answers
GPT-4o mini
The Product Rule of Exponents states that when multiplying two powers with the same base, you add the exponents. Specifically, \( a^m \cdot a^n = a^{m+n} \).
Looking at the response options, we can simplify each one to see if they equal \( 2412 \) when applying the Product Rule:
1. **\( 12^4 \cdot 12^8 \)**:
\[
12^4 \cdot 12^8 = 12^{4+8} = 12^{12}
\]
2. **\( 24^4 \cdot 24^8 \)**:
\[
24^4 \cdot 24^8 = 24^{4+8} = 24^{12}
\]
3. **\( 24^3 \cdot 24^4 \)**:
\[
24^3 \cdot 24^4 = 24^{3+4} = 24^7
\]
4. **\( 64 \cdot 43 \)**:
The bases are different in this case so it doesn’t apply the Product Rule.
None of the expressions directly give \( 2412 \). However, it looks like you may mean \( 24^{12} \). Therefore, the correct response reflecting the Product Rule of Exponents that could lead to a simplified product would be:
**\( 24^4 \cdot 24^8 \) as it simplifies correctly to \( 24^{12} \)**.
Looking at the response options, we can simplify each one to see if they equal \( 2412 \) when applying the Product Rule:
1. **\( 12^4 \cdot 12^8 \)**:
\[
12^4 \cdot 12^8 = 12^{4+8} = 12^{12}
\]
2. **\( 24^4 \cdot 24^8 \)**:
\[
24^4 \cdot 24^8 = 24^{4+8} = 24^{12}
\]
3. **\( 24^3 \cdot 24^4 \)**:
\[
24^3 \cdot 24^4 = 24^{3+4} = 24^7
\]
4. **\( 64 \cdot 43 \)**:
The bases are different in this case so it doesn’t apply the Product Rule.
None of the expressions directly give \( 2412 \). However, it looks like you may mean \( 24^{12} \). Therefore, the correct response reflecting the Product Rule of Exponents that could lead to a simplified product would be:
**\( 24^4 \cdot 24^8 \) as it simplifies correctly to \( 24^{12} \)**.