If the expression 410

Question

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

(412)2
left parenthesis 4 superscript 12 baseline right parenthesis squared

(45)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

(4²)⁸

Answer 1

To simplify the expression \( 4^{10} \) using the Power Rule of Exponents, we need to look for an equivalent form.

The Power Rule states that \( (a^m)^n = a^{mn} \).

Given the options:

1. \( (4^{12})^2 \) simplifies to \( 4^{24} \) (not equivalent to \( 4^{10} \))
2. \( (4^{5})^2 \) simplifies to \( 4^{10} \), which is equivalent!
3. \( 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \) is \( 4^7 \) (not equivalent)
4. \( (4^2)^8 \) simplifies to \( 4^{16} \) (not equivalent)

The correct equivalent expanded expression for \( 4^{10} \) from the options given is:

\( (4^{5})^2 \).