If the expression 410 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)

Question

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

Answer 1

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 $4^{10}$.