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To rewrite the expression \(27^{1/2} \cdot 27^{1/4}\), you can use the property of exponents which states that when multiplying like bases, you add the exponents:
\[
27^{1/2} \cdot 27^{1/4} = 27^{(1/2 + 1/4)}
\]
First, find a common denominator to add \(1/2\) and \(1/4\):
\[
1/2 = 2/4
\]
So,
\[
1/2 + 1/4 = 2/4 + 1/4 = 3/4
\]
Thus, the expression simplifies to:
\[
27^{3/4}
\]
So, \(27^{1/2} \cdot 27^{1/4} = 27^{3/4}\).
Among the options given, the answer is:
**27^{3/4}**.