To simplify the expression \(3^{1/2} \cdot 3^{1/4}\), you can use the property of exponents that states:
\[ a^m \cdot a^n = a^{m+n} \]
In this case, \(a = 3\), \(m = \frac{1}{2}\), and \(n = \frac{1}{4}\).
Now, add the exponents:
\[ \frac{1}{2} + \frac{1}{4} \]
To add these fractions, find a common denominator. The common denominator for 2 and 4 is 4:
\[ \frac{1}{2} = \frac{2}{4} \]
Now add:
\[ \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \]
So, we rewrite the expression as:
\[ 3^{1/2} \cdot 3^{1/4} = 3^{3/4} \]
Thus, the simplified expression is:
\[ \boxed{3^{3/4}} \]