To find the area of the rectangular flower bed, we can use the formula for the area of a rectangle:
\[ \text{Area} = \text{Width} \times \text{Length} \]
The width of the flower bed is \(2^3\) feet and the length is \(2^4\) feet. Now we can substitute these values into the formula:
\[ \text{Area} = 2^3 \times 2^4 \]
Using the property of exponents that states \(a^m \times a^n = a^{m+n}\), we can combine the exponents:
\[ \text{Area} = 2^{3+4} = 2^7 \]
Now, we calculate \(2^7\):
\[ 2^7 = 128 \]
Thus, the area of the flower bed is \(128\) square feet.