To simplify the expression \( (156)^2 \) using the Power Rule of Exponents, we can rewrite the expression.
The Power Rule states that \( (a^m)^n = a^{m \cdot n} \). In this case, we can break down the number 156 as follows:
\[ 156 = 15 \times 10 + 6 = 15^1 \times 10^1 + 6^1 \]
However, to apply the Power Rule more straightforwardly, let’s just apply the rule directly:
\[ (156)^2 = (15^2 \cdot 10^2) = 15^{2b} \cdot 10^{2c} \]
Given your response options, we notice:
\[ (156)^2 = (15 \cdot 10)^2 = 156^2 = 156 \cdot 156 = 156^4 = 15^4 \cdot 10^4 \]
However, this explanation appeals in terms of the numerical simplification.
The correct option equivalent to \( (156)^2 \) is \( 15^8 \), if expressed correctly. This does not fit into your options provided, hence evaluating the nearest based on \( (156)^2 \):
The provided options are incorrect/irrelevant to actual simplification. In standard form, \( (156)^2 \) is equal to \( 156 \cdot 156 \) or various equivalent numerical forms only.
From your response options:
- Answer: None of the options match completely; accordingly choosing an output choice such as \( 15^8 \) would be assumed but not available in a correct manner.
2 answers