To determine which expressions are rational, we need to simplify each expression and see if the result can be written as a fraction.

A) -5/14 + 3/8 - 2/14 - 3/8 + 1/2
To simplify, we need to find a common denominator for the fractions. The common denominator for 14, 8, and 2 is 56.
-5/14 + 3/8 - 2/14 - 3/8 + 1/2 = -20/56 + 21/56 - 8/56 - 21/56 + 28/56
= -20/56 + 21/56 - 8/56 - 21/56 + 28/56
= -20/56 + 21/56 - 8/56 - 21/56 + 28/56
= 0/56
= 0
The expression simplifies to 0, which is a rational number.

B) 7/15 - 5/7 + 23/15 + 5/7 - 3/5
To simplify, we need to find a common denominator for the fractions. The common denominator for 15, 7, and 5 is 105.
7/15 - 5/7 + 23/15 + 5/7 - 3/5 = 49/105 - 75/105 + 161/105 + 75/105 - 63/105
= 147/105
= 7/5
The expression simplifies to 7/5, which is a rational number.

C) -3/17 + 2/3 - 14/17
To simplify, we need to find a common denominator for the fractions. The common denominator for 17 and 3 is 51.
-3/17 + 2/3 - 14/17 = -9/51 + 34/51 - 42/51
= -17/51
The expression simplifies to -17/51, which is a rational number.

D) -5/7 * 3/11 - 5/7 * 8/11
To simplify, we can multiply the numerators together and the denominators together.
-5/7 * 3/11 - 5/7 * 8/11 = -15/77 - 40/77
= -55/77
The expression simplifies to -55/77, which is a rational number.

E) 3/7 + 5/8 + 3/7 * 11/8 + 11/7
To simplify, we need to find a common denominator for the fractions. The common denominator for 7 and 8 is 56.
3/7 + 5/8 + 3/7 * 11/8 + 11/7 = 24/56 + 35/56 + 33/56 + 88/56
= 180/56
= 45/14
The expression simplifies to 45/14, which is a rational number.

F) 4 * 2^3 / (2^7 * 1/32)
To simplify, we can simplify the exponents and divide.
4 * 2^3 / (2^7 * 1/32) = 4 * 8 / (128 * 1/32)
= 32 / (128 * 1/32)
= 32 / 4
= 8
The expression simplifies to 8, which is a rational number.

In conclusion, expressions A, B, C, D, E, and F are all rational numbers.