To simplify 7-5/6•7-7/6, we need to follow the order of operations (PEMDAS) and perform the multiplication and division before addition and subtraction.
7-5/6•7-7/6
= 7 - (5/6) * 7 - (7/6) (Multiplication first)
= 7 - (35/6) - (7/6) (Simplify the multiplication)
= (42/6) - (35/6) - (7/6) (Convert 7 to a fraction with a common denominator)
= (42 - 35 - 7) / 6 (Subtract the numerators)
= 0 / 6
= 0
Therefore, 7-5/6•7-7/6 simplifies to 0.