To use the Power Rule of Exponents, which states that \((a^m)^n = a^{m \cdot n}\), we can rewrite \((156)^2\).
First, notice that \(156\) can be rewritten using its factors. The simplest way to represent \(156\) in terms of \(15\) is to factor it out:
However, more directly, we can just apply the exponent:
\((156)^2\) can be simplified as follows:
\((15 \cdot 10 + 6)^2\) would get complicated since we want it as powers of \(15\).
Here, we look at \(156^2\):
If we can assume \(156 = 15^x\) for simplifying later purposes, we can say:
Moving along, the correct answer using the Power Rule as it is expressed should yield us an expression where the base number (usually the same base) is raised to a power which would generate an ultimate equivalent exponentiation.
However looking at \( (15^x)^2 \), refined, hence we simplify it through steps leading to actually expressing it simply powers of \(15\).
If options given were
- \(15^8\)
- \(15^{12}\)
- \(15^3\)
- \(15^4\)
The correct and equivalent statement strictly should yield out observing 1 of these as future references.
But as we look they don’t simplify correctly thus we recognize they would not yield through our simplistic \(15^{value}\).
Thus if calculating from much further view route it seems none correctly derive from formula observed.
For pure transition of Power Rules, one would mulitply the exponent which is digit raised. The clearer simplification thus cannot fit hence resonates back to zero understanding through until imposing the limted factorials.
Thus upon reviewing closely:
If sooner direct estimation \[ (156)^{2} = [(15.6)^{2} ]\]
Thus should yield \( 15^{(number)}} \)
None of the responses directly achieve clarity though typically we seek:
In conclusion might hence return to align through yielding none thus refer to original values rather than approximating odds light!
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