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

Answer 1

whats the answer

Answer 2

To simplify \(4^{10}\) using the Power Rule of Exponents, we can express it as \((4^2)^5\) because \(4^{10} = (4^2)^{5}\).

Using the Power Rule, which states that \((a^m)^n = a^{m \cdot n}\), we have:

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

So, the expression \(4^{10}\) can also be expanded as \( (4^2)^5 \).

However, when looking at the options provided, the one that represents \(4^{10}\) accurately from the list is:

\((4^2)^8\) is incorrect because \( 2 \cdot 8 = 16 \), not 10.

\((4^5)^2\) is also incorrect because \(5 \cdot 2 = 10\), but you cannot directly relate \(4^5\) squared to \(4^{10}\) without simplification.

The expression \(4 \cdot 4 \cdot 4 \cdots (10 \text{ times})\) accurately represents \(4^{10}\), as it shows the multiplication of \(4\) ten times.

So the most accurate expanded form to represent \(4^{10}\) would be this:

**\(4 \cdot 4 \cdot 4 \cdots (10 \text{ times})\)**

Thus, the best answer given the choices would be the direct expansion of \(4\) multiplied by itself ten times:

\[
4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4
\]

Answer 3

The equivalent expanded expression for \(4^{10}\) using the Power Rule of Exponents is:

**\(4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4\)** (10 times).

If you had to pick from the specific responses given earlier, this representation would accurately simplify to \(4^{10}\).