To rewrite the expression \(2712 \cdot 2714\), we can apply the properties of exponents.
First, we can rewrite \(2712\) and \(2714\) in terms of exponent base \(27\):
\[
2712 = 27^{12} \quad \text{and} \quad 2714 = 27^{14}
\]
Now we can combine these two using the property of exponents:
\[
2712 \cdot 2714 = 27^{12} \cdot 27^{14} = 27^{12 + 14} = 27^{26}
\]
Thus, \(2712 \cdot 2714\) can be rewritten as:
\[
27^{26}
\]
Now, let's evaluate the given options based on this:
1. \(27^{\sqrt{4}} = 27^2\)
2. \(27^{\frac{3}{4}}\)
3. \(27^{\frac{1}{8}}\)
4. \(27^{\sqrt{3}}\)
None of these options matches \(27^{26}\).
Combining in a different way, we can note that:
\[
2712 \cdot 2714 = (27^{13})^2 - 1^2 \quad \text{(using difference of squares)}
\]
Thus, another expression could be given as:
\[
(27^{13})^2 - 1^2 = 27^{26} - 1
\]
In conclusion, the most direct rewriting for the expression is \(27^{26}\). If we need to find a form from the options, none is equivalent to \(27^{26}\).