Question

if the expression 410 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point) Responses (412)2 left parenthesis 4 superscript 12 baseline right parenthesis squared (42)8 left parenthesis 4 squared right parenthesis superscript 8 baseline (45)2 left parenthesis 4 superscript 5 baseline right parenthesis squared 4⋅4⋅4⋅4⋅4⋅4⋅4

Answer 1

To simplify the expression \( 4^{10} \) using the Power Rule of Exponents, we can express it as \( (4^5)^2 \) since \( (a^m)^n = a^{m \cdot n} \) is the Power Rule.

This means we can write:

\[
4^{10} = (4^5)^2
\]

Now, let's look at the response options provided:

1. \( (4^{12})^2 \) – This simplifies to \( 4^{24} \), which is not equivalent.
2. \( (4^2)^8 \) – This simplifies to \( 4^{16} \), which is not equivalent.
3. \( (4^5)^2 \) – This simplifies to \( 4^{10} \), which is equivalent.
4. \( 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \) – This is \( 4^7 \), which is not equivalent.

Among these options, the correct response is:

**\( (4^5)^2 \)** (assuming this option is listed; it is the correct equivalent expanded expression for \( 4^{10} \)).