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 \( 4^{10} \).