Question

If the expression 4^10 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses

(4^2)^8
left parenthesis 4 squared right parenthesis superscript 8 baseline

(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

Answer 1

To simplify \(4^{10}\) using the Power Rule of Exponents, we can express it as \((4^n)^m\) where \(n\) and \(m\) are integers that multiply to give 10.

The options presented are:

1. \((4^2)^8\)
2. \((4^5)^2\)
3. \(4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4\)
4. \((4^{12})^2\)

Now, let's evaluate which expression equals \(4^{10}\):

1. \((4^2)^8 = 4^{2 \cdot 8} = 4^{16}\) (not equivalent)
2. \((4^5)^2 = 4^{5 \cdot 2} = 4^{10}\) (this is equivalent)
3. \(4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 = 4^7\) (not equivalent)
4. \((4^{12})^2 = 4^{12 \cdot 2} = 4^{24}\) (not equivalent)

The correct response, which is an equivalent expanded expression for \(4^{10}\), is:

\((4^5)^2\)