Question

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

(42)8
left parenthesis 4 squared right parenthesis superscript 8 baseline

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

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

4⋅4⋅4⋅4⋅4⋅4⋅4

Answer 1

To simplify the expression \(4^{10}\) using the Power Rule of Exponents, we can express it as \((4^2)^5\) since \(10\) can be written as \(2 \times 5\).

Using the power rule \((a^m)^n = a^{m \cdot n}\), we expand this as:

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

So, \((4^2)^5\) is equivalent to \(4^{10}\), but in the given options, it also forms part of \((4^2)^5\) as \((4^2)^{5}\) is another way to express \(4^{10}\).

The correct equivalent expression among the provided responses is:

\((4^2)^5\)

However, from the options provided, the equivalent expanded expression for \(4^{10}\) is:

**4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4.**

This is the full product indicated in the simplified form. The correct answer is therefore:

**4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4.**