Question

If the expression 4 10 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

(4 2) 8
left parenthesis 4 squared right parenthesis superscript 8 baseline

(4 5) 2
left parenthesis 4 superscript 5 baseline right parenthesis squared

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

Answer 1

To simplify the expression \( 4^{10} \) using the Power Rule of Exponents, we need to recognize that we can express \( 4^{10} \) in terms of its prime factorization. Specifically, \( 4 \) can be rewritten as \( 4^1 \).

The Power Rule states that \( (a^m)^n = a^{m \cdot n} \). Thus, if we rewrite \( 4 \) in terms of its power, we have \( 4 = 4^1 \).

However, for one of the provided options to be equivalent to \( 4^{10} \), we must check if any transformation matches \( 4^{10} \).

Let's analyze the options:
1. **\( 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \)**: This translates to \( 4^7 \), which is not \( 4^{10} \).

2. **\( (4^2)^8 \)**: Using the Power Rule, this simplifies to \( 4^{2 \cdot 8} = 4^{16} \), which is not \( 4^{10} \).

3. **\( (4^5)^2 \)**: This simplifies to \( 4^{5 \cdot 2} = 4^{10} \), which is correct.

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

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

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