If the expression 410 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 (45)2 left parenthesis 4 superscript 5 baseline right parenthesis squared (412)2 left parenthesis 4 superscript 12 baseline right parenthesis squared (42)8

1 answer

To simplify the expression \(410\) using the Power Rule of Exponents, we can express \(410\) as \(4^{10}\).

Using the Power Rule of Exponents, \(a^{m \cdot n} = (a^m)^n\), we can interpret \(4^{10}\) in terms of smaller exponents if needed.

However, if the intention is to expand \(4^{10}\), that would simply lead to \(4\) multiplied by itself \(10\) times:

\[ 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \]

This corresponds to one of the answers, which is \(4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4\) or explicitly stated as "4 times 4 times 4 times 4 times 4 times 4 times 4".

Thus, the equivalent expanded expression for \(4^{10}\) is:

Response: \(4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4\) (4 times 4 times 4 times 4 times 4 times 4 times 4)