To rewrite the expression \( 27 \frac{1}{2} \cdot 27 \frac{1}{4} \), we first convert the mixed numbers to improper fractions:
- \( 27 \frac{1}{2} = 27 + \frac{1}{2} = 27.5 \) or \( \frac{55}{2} \)
- \( 27 \frac{1}{4} = 27 + \frac{1}{4} = 27.25 \) or \( \frac{109}{4} \)
Now we multiply:
\[ \frac{55}{2} \cdot \frac{109}{4} = \frac{55 \cdot 109}{2 \cdot 4} = \frac{5995}{8} \]
Now, we convert it back into a mixed number:
\( 5995 \div 8 = 749 \) with a remainder of \( 3 \), so:
\[ \frac{5995}{8} = 749 \frac{3}{8} \]
Thus, the result of \( 27 \frac{1}{2} \cdot 27 \frac{1}{4} \) can be expressed as \( 749 \frac{3}{8} \).
However, from the responses provided, the correct rewritten form of the multiplication in simpler fractions allows us to understand it differently which can lead to \( 27^{3/4} \).
Therefore, from the options, the rewritten form similar to the multiplication and directly assessing roots offers measurable forms answering to:
- Response: \( 27^{3/4} \)