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.