Question
If the expression 410 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses
4⋅4⋅4⋅4⋅4⋅4⋅4
4 times 4 times 4 times 4 times 4 times 4 times 4
(42)8
left parenthesis 4 squared right parenthesis superscript 8 baseline
(412)2
left parenthesis 4 superscript 12 baseline right parenthesis squared
(45)2
Responses
4⋅4⋅4⋅4⋅4⋅4⋅4
4 times 4 times 4 times 4 times 4 times 4 times 4
(42)8
left parenthesis 4 squared right parenthesis superscript 8 baseline
(412)2
left parenthesis 4 superscript 12 baseline right parenthesis squared
(45)2
Answers
GPT-4o mini
To simplify the expression \( 4^{10} \) using the Power Rule of Exponents, we can express it as \( (4^2)^5 \). This means that we can use the property of exponents where \( (a^m)^n = a^{m \cdot n} \).
Given the options provided, \( (4^2)^5 \) can be expanded to:
\[
(4^2)^5 = 4^{2 \cdot 5} = 4^{10}
\]
However, none of the provided responses seem to explicitly match this form directly.
Let's analyze the given options:
1. **4⋅4⋅4⋅4⋅4⋅4⋅4** - This is \( 4^7 \).
2. **(42)8** - This simplifies to \( 4^{16} \).
3. **(412)2** - This simplifies to \( 4^{12} \).
4. **(45)2** - This simplifies to \( 4^{10} \).
Among these, the correct equivalent expanded expression for \( 4^{10} \) is:
**(45)2**
Thus, the answer is \( (4^5)^2 \) which equals \( 4^{10} \).
Given the options provided, \( (4^2)^5 \) can be expanded to:
\[
(4^2)^5 = 4^{2 \cdot 5} = 4^{10}
\]
However, none of the provided responses seem to explicitly match this form directly.
Let's analyze the given options:
1. **4⋅4⋅4⋅4⋅4⋅4⋅4** - This is \( 4^7 \).
2. **(42)8** - This simplifies to \( 4^{16} \).
3. **(412)2** - This simplifies to \( 4^{12} \).
4. **(45)2** - This simplifies to \( 4^{10} \).
Among these, the correct equivalent expanded expression for \( 4^{10} \) is:
**(45)2**
Thus, the answer is \( (4^5)^2 \) which equals \( 4^{10} \).