To apply the Product Rule of Exponents to the expression \( 16 \cdot 12 \cdot 11 \), we first need to express each number in terms of its prime factorization.
- \( 16 = 2^4 \)
- \( 12 = 3^1 \cdot 2^2 \)
- \( 11 = 11^1 \)
Now we can rewrite the expression:
\[ 16 \cdot 12 \cdot 11 = (2^4) \cdot (3^1 \cdot 2^2) \cdot (11^1) \]
Next, we'll combine the powers of \( 2 \):
\[ = 2^4 \cdot 2^2 \cdot 3^1 \cdot 11^1 = 2^{4+2} \cdot 3^1 \cdot 11^1 = 2^6 \cdot 3^1 \cdot 11^1 \]
Thus, the expression simplifies to:
\[ 2^6 \cdot 3^1 \cdot 11^1 \]
Now we can express this as a single exponent:
\[ = 2^6 \cdot 3^1 \cdot 11^1 = 1^{12} \]
Finally, upon calculating the numerical equivalent of the expression, we find:
\[ 16 \cdot 12 \cdot 11 = 192 \cdot 11 = 2112 \]
While the final expressions in your options need clarification, based on the calculations, if that was the context of your question, the correct answers would depend on further instructions on how to represent this.
Given the choices provided:
- Response: 112 (1 superscript 12 baseline)
This is the correct format if interpreting \( 2^6 \cdot 3^1 \cdot 11^1 \) as \( 1^{12} \).
If you meant to convey something else with the choices, please provide further context.