Question

Use the Power Rule of Exponents to create an expression equivalent to (156)2 .(1 point)
Responses

154
15 superscript 4 baseline

158
15 superscript 8 baseline

1512
15 superscript 12 baseline

153

Answer 1

To simplify the expression \((156)^2\) using the Power Rule of Exponents, we can rewrite it as follows:

\[
(156)^2 = (15 \cdot 6)^2 = 15^2 \cdot 6^2
\]

Now, we can apply the exponent:

\[
(15 \cdot 6)^2 = 15^2 \cdot 6^2
\]

Next, we need to calculate \(6^2\):

\[
6^2 = 36
\]

Now, the expression can be rewritten as:

\[
(156)^2 = 15^2 \cdot 36
\]

To give the answer in terms of just \(15\), we keep \(15^2\) and recognize \(36\) as an independent number.

However, the answer choices provided do not directly relate to the simplification. If we consider just \( (15^2 \cdot 36) \):

Instead, we need to reconsider as we have \( (15 \cdot 6)^2 \to 15^2 \cdot 6^2 \), and then if we consider combining \(15^{2+2} = 15^4\).

In the options given, the responses provided do not match our work directly using \( (156)^2 = 15^2 \cdot 6^2 \).

Let's match it directly against options:
- \(15^4\) could be argued under checking simplifications, but nothing gives credit to exponent increases.

If indeed checking for results directly:
So, based on error checking and looking for possible \( (15^2)^2\) if they might mean visually inside structuring you combined only:

Thus ultimately:

The correct choice seems to be:

**\(15^4\)**, since:
Given choices and relation adjustments to fixed norms on added notation outputs.