If the expression 4^10

Question

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

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

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

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

(4^2)^8

Answer 1

To simplify the expression \(4^{10}\) using the Power Rule of Exponents, we can express it in a way that shows how it's derived from another exponent. The Power Rule states that \((a^m)^n = a^{m \cdot n}\).

Among the options given, \((4^5)^2\) is an equivalent expression because:

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

The other options do not represent \(4^{10}\) when simplified, so the correct answer is:

(4^5)^2