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 (42)8 left parenthesis 4 squared right parenthesis superscript 8 baseline (45)2 left parenthesis 4 superscript 5 baseline right parenthesis squared (412)2

Answer 1

To simplify \( 410 \) using the Power Rule of Exponents, we first need to understand that it represents \( 4^{10} \).

Using the properties of exponents, we can express \( 4^{10} \) in several equivalent forms.

1. Expanding using multiplication:
   • \( 4^{10} \) can be expressed as \( 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \), which is the expanded form (this is equivalent to \( 4 \) multiplied by itself \( 10 \) times):
   • Answer: \( 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \).

The other options represent different forms of \( 4^{10} \), but only the first option is the straightforward expansion. So, the equivalent expanded expression for \( 410 \) using the Power Rule of Exponents is:

\( 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \).