To combine the expression \( 27^{1/2} \cdot 27^{1/4} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
So, we have:
\[ 27^{1/2} \cdot 27^{1/4} = 27^{1/2 + 1/4} \]
Now, we need to add the exponents \( \frac{1}{2} + \frac{1}{4} \). To do this, we can convert \( \frac{1}{2} \) to a fraction with a denominator of 4:
\[ \frac{1}{2} = \frac{2}{4} \]
Now we can add:
\[ \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \]
Putting it all together:
\[ 27^{1/2} \cdot 27^{1/4} = 27^{3/4} \]
Thus, the combined expression is \( 27^{3/4} \).
So, the combined expression is 27 to the power of \( \frac{3}{4} \).
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