Question
Apply the Product Rule of Exponents to form an equivalent expression of 16⋅12⋅11
.(1 point)
Responses
113
1 superscript 13 baseline
19
1 superscript 9 baseline
13
1 cubed
112
.(1 point)
Responses
113
1 superscript 13 baseline
19
1 superscript 9 baseline
13
1 cubed
112
Answers
GPT-4o mini
To apply the Product Rule of Exponents to the expression \( 16 \cdot 12 \cdot 11 \), first break down each number into its prime factors.
1. **Prime factorization**:
- \( 16 = 2^4 \)
- \( 12 = 2^2 \cdot 3^1 \)
- \( 11 = 11^1 \)
2. **Combine the factors**:
\[
16 \cdot 12 \cdot 11 = (2^4) \cdot (2^2 \cdot 3^1) \cdot (11^1)
\]
3. **Rearrange and combine like bases**:
\[
= 2^{4+2} \cdot 3^1 \cdot 11^1 = 2^6 \cdot 3^1 \cdot 11^1
\]
This simplifies to \( 64 \cdot 3 \cdot 11 \). However, let's focus on presenting the product of the original numbers if we need an exponent form.
The product of \( 16, 12, \) and \( 11 \) does not result simply in an expression with a single exponent form.
However, on reviewing your answer choices, I assume you want to consider the total exponent of each distinct base present in the product. Given those choices, a synthesized value seems necessary for clarity or the closest equivalent factor combinations may also be reflected accordingly.
Your question may imply an alternative context here where you expect simply structured responses leading toward an equivalent exponent solution. Based solely on interpretations of base structures, none of the provided options can derive naturally from a direct multiplication of 16, 12, and 11 when looking purely at summed exponents alone.
That said, the most fitting of your answer options toward an estimation if equivalency to powers were examined as such would simply be checking one of those listed forms when the intent of ambiguity remains.
However, please clarify or adjust what represented results better suit resulting numbers, so I can assist you in content that meets stood evaluations properly.
1. **Prime factorization**:
- \( 16 = 2^4 \)
- \( 12 = 2^2 \cdot 3^1 \)
- \( 11 = 11^1 \)
2. **Combine the factors**:
\[
16 \cdot 12 \cdot 11 = (2^4) \cdot (2^2 \cdot 3^1) \cdot (11^1)
\]
3. **Rearrange and combine like bases**:
\[
= 2^{4+2} \cdot 3^1 \cdot 11^1 = 2^6 \cdot 3^1 \cdot 11^1
\]
This simplifies to \( 64 \cdot 3 \cdot 11 \). However, let's focus on presenting the product of the original numbers if we need an exponent form.
The product of \( 16, 12, \) and \( 11 \) does not result simply in an expression with a single exponent form.
However, on reviewing your answer choices, I assume you want to consider the total exponent of each distinct base present in the product. Given those choices, a synthesized value seems necessary for clarity or the closest equivalent factor combinations may also be reflected accordingly.
Your question may imply an alternative context here where you expect simply structured responses leading toward an equivalent exponent solution. Based solely on interpretations of base structures, none of the provided options can derive naturally from a direct multiplication of 16, 12, and 11 when looking purely at summed exponents alone.
That said, the most fitting of your answer options toward an estimation if equivalency to powers were examined as such would simply be checking one of those listed forms when the intent of ambiguity remains.
However, please clarify or adjust what represented results better suit resulting numbers, so I can assist you in content that meets stood evaluations properly.