which of the following Expression shows that rational numbers are associative under multiplication ?a= (2/3)×((_6/7)×(3/7)))=(((2/3)×(_6/7))×(3/5)

To show that rational numbers are associative under multiplication, we need to demonstrate that the two expressions you provided are equal. Let's evaluate the expressions: a = (2/3) × ((6/7) × (3/7)) b = ((2/3) × (6/7)) × (3/5) Expression a: a = (2/3) × ((6/7) × (3/7)) a = (2/3) × (18/49) (simplify the inner multiplication) a = 36/147 (multiply the numerators and denominators) a = 4/7 (simplify the fraction) Expression b: b = ((2/3) × (6/7)) × (3/5) b = (12/21) × (3/5) (simplify the inner multiplication) b = 36/105 (multiply the numerators and denominators) b = 12/35 (simplify the fraction) As a and b do not yield the same result, the given expressions do not show that rational numbers are associative under multiplication.