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}.
1 answer