To solve this expression, we follow the order of operations (also known as PEMDAS).

First, we simplify the exponent (-1)^6. Since any number raised to an even power is positive, (-1)^6 equals 1.

Next, we simplify (3/4)^2. To square a fraction, we square the numerator and the denominator separately. (3/4)^2 = (3^2)/(4^2) = 9/16.

Finally, we subtract 3/8 from the previous result. To subtract fractions, we need a common denominator. The common denominator for 9/16 and 3/8 is 16. So, we have (9/16) - (3/8) = (9/16) - (6/16) = 3/16.

Therefore, the simplified expression is 1 + 3/16 = 16/16 + 3/16 = 19/16.