Question
Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses
(−5)0
(
−
5
)
0
left parenthesis negative 5 right parenthesis superscript 0 baseline
(74)8
(
7
4
)
8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline
129
12
9
12 superscript 9 baseline
(78)⋅(710)
Responses
(−5)0
(
−
5
)
0
left parenthesis negative 5 right parenthesis superscript 0 baseline
(74)8
(
7
4
)
8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline
129
12
9
12 superscript 9 baseline
(78)⋅(710)
Answers
Answer
Which of the following correctly used the Power Rule of Exponents in the expression (109)7
(
10
9
)
7
?(1 point)
Responses
102
10
2
10 superscript 2 baseline
907
90
7
90 superscript 7 baseline
1063
10
63
10 superscript 63 baseline
1016
10
16
10 superscript 16 baseline
(
10
9
)
7
?(1 point)
Responses
102
10
2
10 superscript 2 baseline
907
90
7
90 superscript 7 baseline
1063
10
63
10 superscript 63 baseline
1016
10
16
10 superscript 16 baseline
Answer
If the expression 410
4
10
was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses
(45)2
(
4
5
)
2
left parenthesis 4 superscript 5 baseline right parenthesis squared
4⋅4⋅4⋅4⋅4⋅4⋅4
4
⋅
4
⋅
4
⋅
4
⋅
4
⋅
4
⋅
4
4 times 4 times 4 times 4 times 4 times 4 times 4
(42)8
(
4
2
)
8
left parenthesis 4 squared right parenthesis superscript 8 baseline
(412)2
4
10
was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses
(45)2
(
4
5
)
2
left parenthesis 4 superscript 5 baseline right parenthesis squared
4⋅4⋅4⋅4⋅4⋅4⋅4
4
⋅
4
⋅
4
⋅
4
⋅
4
⋅
4
⋅
4
4 times 4 times 4 times 4 times 4 times 4 times 4
(42)8
(
4
2
)
8
left parenthesis 4 squared right parenthesis superscript 8 baseline
(412)2
Answer
Use the Power Rule of Exponents to create an expression equivalent to (156)2
(
15
6
)
2
.(1 point)
Responses
154
15
4
15 superscript 4 baseline
1512
15
12
15 superscript 12 baseline
158
15
8
15 superscript 8 baseline
153
(
15
6
)
2
.(1 point)
Responses
154
15
4
15 superscript 4 baseline
1512
15
12
15 superscript 12 baseline
158
15
8
15 superscript 8 baseline
153
Answer
What exponent would make the two expressions equivalent: (33)x=324
(
3
3
)
𝑥
=
3
24
?(1 point)
Responses
8
8
21
21
27
27
15
(
3
3
)
𝑥
=
3
24
?(1 point)
Responses
8
8
21
21
27
27
15
Answered by
GPT-4o mini
The expression that is correctly developed to use the Power Rule of Exponents is:
\((7^4)^8\)
This expression applies the Power Rule, which states that \((a^m)^n = a^{m \cdot n}\). When applying this rule to the expression \((7^4)^8\), you would multiply the exponents, resulting in \(7^{4 \cdot 8} = 7^{32}\).
The other options do not correctly illustrate the Power Rule of Exponents as clearly.
\((7^4)^8\)
This expression applies the Power Rule, which states that \((a^m)^n = a^{m \cdot n}\). When applying this rule to the expression \((7^4)^8\), you would multiply the exponents, resulting in \(7^{4 \cdot 8} = 7^{32}\).
The other options do not correctly illustrate the Power Rule of Exponents as clearly.
Answered by
GPT-4o mini
The expression \((10^9)^7\) correctly uses the Power Rule of Exponents, which states that \((a^m)^n = a^{m \cdot n}\).
Applying this rule:
\[
(10^9)^7 = 10^{9 \cdot 7} = 10^{63}
\]
Thus, the correct response is:
**\(10^{63}\)** (10 superscript 63).
Applying this rule:
\[
(10^9)^7 = 10^{9 \cdot 7} = 10^{63}
\]
Thus, the correct response is:
**\(10^{63}\)** (10 superscript 63).
Answered by
GPT-4o mini
To simplify \(4^{10}\) using the Power Rule of Exponents, we can express it as an equivalent expanded expression.
The simplest expansion of \(4^{10}\) is:
**\(4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4\)** (which is \(4\) multiplied by itself \(10\) times).
So the correct response from your options would be:
**\(4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4\)** (4 times 4 times 4 times 4 times 4 times 4 times 4).
The other options either do not represent \(4^{10}\) correctly or are incorrect forms of the original expression.
The simplest expansion of \(4^{10}\) is:
**\(4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4\)** (which is \(4\) multiplied by itself \(10\) times).
So the correct response from your options would be:
**\(4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4\)** (4 times 4 times 4 times 4 times 4 times 4 times 4).
The other options either do not represent \(4^{10}\) correctly or are incorrect forms of the original expression.
Answered by
GPT-4o mini
To simplify the expression \((15^6)^2\) using the Power Rule of Exponents, we apply the rule which states that \((a^m)^n = a^{m \cdot n}\).
Here, we have:
\[
(15^6)^2 = 15^{6 \cdot 2} = 15^{12}
\]
So, the equivalent expression is:
**\(15^{12}\)** (15 superscript 12).
Therefore, the correct response is:
**1512**.
Here, we have:
\[
(15^6)^2 = 15^{6 \cdot 2} = 15^{12}
\]
So, the equivalent expression is:
**\(15^{12}\)** (15 superscript 12).
Therefore, the correct response is:
**1512**.
Answered by
GPT-4o mini
To find the value of \( x \) that makes the two expressions equivalent, you can follow these steps:
Given the equation:
\[
(3^3)^x = 3^{24}
\]
Using the Power Rule of Exponents, we can simplify the left side:
\[
3^{3x} = 3^{24}
\]
Since the bases (3) are the same, we can set the exponents equal to each other:
\[
3x = 24
\]
Now, solve for \( x \):
\[
x = \frac{24}{3} = 8
\]
Thus, the correct exponent that makes the two expressions equivalent is:
**8**.
Given the equation:
\[
(3^3)^x = 3^{24}
\]
Using the Power Rule of Exponents, we can simplify the left side:
\[
3^{3x} = 3^{24}
\]
Since the bases (3) are the same, we can set the exponents equal to each other:
\[
3x = 24
\]
Now, solve for \( x \):
\[
x = \frac{24}{3} = 8
\]
Thus, the correct exponent that makes the two expressions equivalent is:
**8**.