Using the Power Rule of Exponents, what is an equivalent form of (2^8)^2 ?(1 point)

Question

Responses

2(8÷2)
2 superscript left parenthesis 8 divided by 2 right parenthesis baseline

2(8⋅2)
2 superscript left parenthesis 8 times 2 right parenthesis baseline

2(8+2)
2 superscript left parenthesis 8 plus 2 right parenthesis baseline

2(8−2)

Answer 1

To simplify \( (2^8)^2 \) using the Power Rule of Exponents, which states that \( (a^m)^n = a^{m \cdot n} \), we can apply the rule:

\[ (2^8)^2 = 2^{8 \cdot 2} = 2^{16} \]

This means that the equivalent form of \( (2^8)^2 \) is \( 2^{(8 \cdot 2)} \).

Therefore, the correct response from your options is:

2 superscript left parenthesis 8 times 2 right parenthesis baseline (which represents \( 2^{(8 \cdot 2)} \)).