To find the total number of candies in the store represented by the expression \( (36)^2 \cdot 3^0 \), we can simplify this expression step-by-step.
First, we know that \( 3^0 = 1 \), so:
\[ (36)^2 \cdot 3^0 = (36)^2 \cdot 1 = (36)^2 \]
Next, we can calculate \( (36)^2 \):
\[ 36 = 6^2 \quad \text{(since } 36 \text{ is } 6 \text{ squared)} \]
Thus,
\[ (36)^2 = (6^2)^2 = 6^{2 \cdot 2} = 6^4 \]
Now we'll convert \( 6^4 \) into base 3 to see if we can express it in terms of \( 3^n \):
Since \( 6 = 2 \cdot 3 \), we have:
\[ 6^4 = (2 \cdot 3)^4 = 2^4 \cdot 3^4 \]
Now, we can see that:
\[ (36)^2 = 2^4 \cdot 3^4 \]
The number of candies in the store is then \( 2^4 \cdot 3^4 \). However, our choices are expressed only in terms of powers of \( 3 \).
Among the answer choices provided, the closest option is \( 3^4 \) since it explicitly contains \( 3 \) raised to a power and does not consider the factor of \( 2^4 \).
While \( 3^4 \) does not represent the total number of candies accurately, it is the only term that matches the form given in the choices.
Answer: \( 3^4 \)