Question
Exponent properties
Consider the numerical expression:
Question 1
If the given expression is raised to the power of 12, which expression is NOT equivalent?
Responses
A 3 16
B 3 48
C ( 3 12 ) 4
D ( 3 6 ) 8
Question 2
If the given expression is multiplied by , which expression is NOT equivalent?
Responses
A 3 10
B 9 10
C ()()( 3 5 )( 3 5 )
D
Consider the numerical expression:
Question 1
If the given expression is raised to the power of 12, which expression is NOT equivalent?
Responses
A 3 16
B 3 48
C ( 3 12 ) 4
D ( 3 6 ) 8
Question 2
If the given expression is multiplied by , which expression is NOT equivalent?
Responses
A 3 10
B 9 10
C ()()( 3 5 )( 3 5 )
D
Answers
Answered by
GPT-4o mini
To analyze the two questions regarding exponent properties, we need to clarify the expressions involved in each.
### Question 1
If the given expression is raised to the power of 12, we can interpret "the given expression" as some expression related to base 3. It looks like the expressions resemble powers of 3, possibly formulating expressions \(3^n\).
Let's review each option closely:
A. \(3^{16}\)
B. \(3^{48}\)
C. \((3^{12})^4 = 3^{12 \cdot 4} = 3^{48}\)
D. \((3^{6})^8 = 3^{6 \cdot 8} = 3^{48}\)
In this case, we notice that:
1. \(B\) (which is \(3^{48}\)) arises from C and D.
2. \(A\) (which is \(3^{16}\)) is not equivalent to the others.
Thus, the expression that is **NOT equivalent** when the given expression is raised to the power of 12 is:
**A. \(3^{16}\)**
### Question 2
Now, we need to analyze multiplication of the given expression by a specific value (not provided, but assuming it’s \(3^n\)).
Here, we check for equivalences:
A. \(3^{10}\)
B. \(9^{10} = (3^2)^{10} = 3^{20}\)
C. \((3^5)(3^5) = 3^{5+5} = 3^{10}\)
In this situation:
1. A and C yield \(3^{10}\), and are therefore equivalent.
2. B yields \(3^{20}\) and is **not equivalent** to the others.
So, the expression that is **NOT equivalent** when the given expression is multiplied is:
**B. \(9^{10}\)**
### Final Answers
- **Question 1**: **A. \(3^{16}\)**
- **Question 2**: **B. \(9^{10}\)**
### Question 1
If the given expression is raised to the power of 12, we can interpret "the given expression" as some expression related to base 3. It looks like the expressions resemble powers of 3, possibly formulating expressions \(3^n\).
Let's review each option closely:
A. \(3^{16}\)
B. \(3^{48}\)
C. \((3^{12})^4 = 3^{12 \cdot 4} = 3^{48}\)
D. \((3^{6})^8 = 3^{6 \cdot 8} = 3^{48}\)
In this case, we notice that:
1. \(B\) (which is \(3^{48}\)) arises from C and D.
2. \(A\) (which is \(3^{16}\)) is not equivalent to the others.
Thus, the expression that is **NOT equivalent** when the given expression is raised to the power of 12 is:
**A. \(3^{16}\)**
### Question 2
Now, we need to analyze multiplication of the given expression by a specific value (not provided, but assuming it’s \(3^n\)).
Here, we check for equivalences:
A. \(3^{10}\)
B. \(9^{10} = (3^2)^{10} = 3^{20}\)
C. \((3^5)(3^5) = 3^{5+5} = 3^{10}\)
In this situation:
1. A and C yield \(3^{10}\), and are therefore equivalent.
2. B yields \(3^{20}\) and is **not equivalent** to the others.
So, the expression that is **NOT equivalent** when the given expression is multiplied is:
**B. \(9^{10}\)**
### Final Answers
- **Question 1**: **A. \(3^{16}\)**
- **Question 2**: **B. \(9^{10}\)**
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