Use the Power Rule of Exponents to create an expression equivalent to (156)2

To use the Power Rule of Exponents, which states that \((a^m)^n = a^{m \cdot n}\), we can rewrite \((156)^2\).

We can express 156 as \(15 \times 10 + 6\) and observe that it's not straightforward for applying the power rule directly. However, we consider it as a composite of factors.

From the options given, it seems we can also interpret \(156\) as \(15^k\) though here we need to focus on speed of math.

If you rewrite \(156\) in terms of its prime factors, we see that \(156 = 3 \times 52 = 3 \times 4 \times 13\), which does not directly give a manageable power of 15.

Instead, let's focus on the provided potential answers which relate to powers of \(15\).

Given the expression \( (156)^2 \), the equivalent expression that follows the exponent rules should be represented as something like:

• \((156)^2 = (15.6)^2\), but we are checking \(15^k\).

In looking at your options, none align perfectly with \( (156)^2 = (15^4) \), it appears \(15^8\) could be written by exponent manipulation.

But analyzing for \(15^2\) or more fractional compositions is needed for a consistent match.

Directly relating: \[ 156^2 = (15^8) \]

So the answer would state:

Option : \(15^8\), recommending explicity to indicate provided options.

Thus, the correct selection is :

15 to the power of 8.