Question

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

Answer 1

To simplify the expression \( 410 \) using the Power Rule of Exponents, we start by recognizing that the expression represents \( 4^{10} \).

Using the Power Rule, \( a^{mn} = (a^m)^n \), we can rewrite \( 4^{10} \) in different equivalent forms.

From the provided options, we see that we need to break down \( 4^{10} \) into possibly different parts to match the choices.

1. The expression \( (4^5)^2 \) simplifies back to \( 4^{10} \) because \( 4^5 \times 4^5 = 4^{10} \).
2. The expression \( (4^{12})^2 \) simplifies to \( 4^{24} \) which is not \( 4^{10} \).
3. The expression \( (4^2)^8 \) simplifies to \( 4^{16} \) which is not \( 4^{10} \).
4. The expression \( 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \) represents \( 4^{10} \) as it multiplies \( 4 \) ten times.

Among these, the correct answer that represents \( 4^{10} \) using the Power Rule of Exponents is:

(4^5)^2.