Question

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

(42)8
left parenthesis 4 squared right parenthesis superscript 8 baseline

(412)2
left parenthesis 4 superscript 12 baseline right parenthesis squared

4⋅4⋅4⋅4⋅4⋅4⋅4
4 times 4 times 4 times 4 times 4 times 4 times 4

(45)2

Answer 1

To simplify the expression \( 4^{10} \) using the Power Rule of Exponents, we can express it in alternative forms.

The Power Rule states that \( (a^m)^n = a^{m \cdot n} \).

Let’s evaluate each option:

1. \( (4^2)^8 \) – This simplifies to \( 4^{2 \cdot 8} = 4^{16} \), which is not equivalent to \( 4^{10} \).

2. \( (4^{12})^2 \) – This simplifies to \( 4^{12 \cdot 2} = 4^{24} \), which is also not equivalent to \( 4^{10} \).

3. \( 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \) – This represents \( 4^7 \), which is not equivalent to \( 4^{10} \).

4. \( (4^5)^2 \) – This simplifies to \( 4^{5 \cdot 2} = 4^{10} \), which is equivalent to \( 4^{10} \).

Therefore, the correct option that is equivalent to the expression \( 4^{10} \) is:

**\( (4^5)^2 \)**.