(9)÷(5/4)×(7/9)×(-5)÷(7/2)

To evaluate the expression (9)÷(5/4)×(7/9)×(-5)÷(7/2), we follow the order of operations, which is parentheses, multiplication and division from left to right.

First, let's simplify the expression within the parentheses.
(9)÷(5/4) = 9 ÷ (5/4) = 9 × (4/5) = 9 × 4/5 = 36/5

Now, let's simplify the multiplication and division from left to right.
(36/5) × (7/9) × (-5) ÷ (7/2)

Cancel out common factors:
(36/5) × (1/9) × (-1) ÷ (1/2)

Multiply the numerators:
(36 ×1 ×(-1)) / (5 × 9 × 1/2)

Multiply the denominators:
(36 × -1) / (5 × 9 × 1/2)

Simplify:
-36 / (45 × 1/2)
= -36 / (45/2)

To divide by a fraction, we multiply by its reciprocal:
= -36 × (2/45)
= -72/45

Simplify the fraction:
= -8/5

To solve this expression step-by-step, let's start with the division:

(9) ÷ (5/4)

To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 5/4 is 4/5, so we have:

(9) × (4/5)

Multiplying 9 by 4 gives us 36:

36/5

Next, let's multiply this result by (7/9):

(36/5) × (7/9)

When multiplying fractions, we multiply the numerators together and the denominators together, which gives us:

(36 * 7)/(5 * 9)
252/45

Simplifying this fraction, we can see that both 252 and 45 are divisible by 9:

(252 ÷ 9) / (45 ÷ 9)
28/5

Finally, let's multiply this fraction by (-5) and divide it by (7/2):

(28/5) × (-5) ÷ (7/2)

To multiply fractions, we simply multiply the numerators and multiply the denominators:

(28 * -5) / (5 * 1) ÷ (7/2)
-140/5 ÷ (7/2)

To divide by a fraction, we can multiply by the reciprocal:

(-140/5) × (2/7)

Multiplying -140 by 2 gives us -280:

-280/5

This fraction can be simplified by dividing both the numerator and denominator by 5:

(-280 ÷ 5) / (5 ÷ 5)
-56/1

Therefore, the final result is -56.