Answer:
Explanation:
To simplify this expression, we can first simplify each fraction separately, and then divide the resulting fractions.
40mn/18r^2 can be simplified by dividing the numerator and denominator by the greatest common factor, which is 2:
40mn/18r^2 = (20m/9r)^2
25m^2n/27r^2m can be simplified by dividing the numerator and denominator by the greatest common factor, which is m:
25m^2n/27r^2m = (25mn/27r^2)
So, the expression becomes:
(20m/9r)^2 ÷ (25mn/27r^2)
To divide fractions, we can multiply by the reciprocal of the second fraction:
(20m/9r)^2 × (27r^2/25mn)
Simplifying each fraction, we get:
(400m^2/81r^2) × (27r^2/25mn)
Multiplying the numerators and denominators separately, we get:
(400m^2 × 27r^2)/(81r^2 × 25mn)
Simplifying further, we get:
(4m^2 × 27)/(9mn)
Multiplying the numerator and denominator by 3, we get:
(4m^2 × 27 × 3)/(9mn × 3) = (36m^2)/(3mn)
Simplifying further, we get:
12m/n
Therefore, the simplified expression is 12m/n.