The notation \( 27^{4/3} \) can be interpreted as raising 27 to the power of \( \frac{4}{3} \).
Given that the cube root of 27 is 3, we can rewrite 27 as \( 3^3 \). Thus:
\[ 27^{4/3} = (3^3)^{4/3} = 3^{3 \cdot \frac{4}{3}} = 3^4 \]
Now we need to calculate \( 3^4 \):
\[ 3^4 = 3 \times 3 \times 3 \times 3 = 9 \times 3 = 27 \times 3 = 81 \]
So, \( 27^{4/3} = 81 \).
The correct answer is 81.