To simplify the expression \( (156)^2 \) using the Power Rule of Exponents, we can apply the rule that states \( (a^m)^n = a^{m \cdot n} \).
In your expression, \( 156^2 \) can be rewritten as:
\[ (15^1 \cdot 6^1)^2 = 15^{2 \cdot 1} \cdot 6^{2 \cdot 1} = 15^2 \cdot 6^2 \]
However, the expression \( (156)^2 \) represents \( 156 \) raised to the power of \( 2 \), which simply equals \( 156^2 \) is not reducible in the given terms.
None of the provided options \( 1512 \), \( 15^{12} \), \( 15^{8} \), \( 15^{4} \), or \( 15^{3} \) seem to relate specifically to \( (156)^2 \) itself in direct exponentiation of \( 156 \).
If we look at the options provided, perhaps you were supposed to consider a different base, or they may have been intended to express a result that corresponds better to a transformation of the numerical values (like calculating directly).
Is there a specific aspect of the calculation you want to clarify?