Question

4/5*10/11,. 3/7*18/19. 4/45:(12/25-4/15)+15/16*4/13 (1/3-1/4)в 2 степ. *(1/6) в 3 степ.

Answer 1

4/5*10/11= 8/11
3/7*18/19= 54/133
4/45:(12/25-4/15)+15/16*4/13= 459/260
(1/3-1/4)в 2 степ. *(1/6) в 3 степ.= 1/31104

Answer 2

Let's solve each of the expressions step by step:

1. 4/5 * 10/11: (4/5) * (10/11) = 40/55 = 8/11

2. 3/7 * 18/19: (3/7) * (18/19) = 54/133

3. 4/45 : (12/25 - 4/15) + 15/16 * 4/13: Step 1: Simplify the expression inside the parenthesis: (12/25 - 4/15) = (12/25) - (4/15) To subtract fractions, find a common denominator, which is 75 in this case: = (12/25 * 3/3) - (4/15 * 5/5) = (36/75) - (20/75) = (36 - 20) / 75 = 16/75

   Step 2: Divide 4/45 by the result of the simplified expression: 4/45 : (16/75) = 4/45 * (75/16) = (4 * 75) / (45 * 16) = 300 / 720 = 5/12

   Step 3: Multiply 15/16 by 4/13: (15/16) * (4/13) = 60/208

   Step 4: Add the results of the previous steps: 5/12 + 60/208 = (5 * 17) / (12 * 17) + 60/208 = (85 + 60) / 208 = 145 / 208

4. (1/3 - 1/4)^2 * (1/6)^3: Step 1: Simplify the expression inside the parenthesis: (1/3 - 1/4) = (4/12 - 3/12) = 1/12

   Step 2: Square the result: (1/12)^2 = (1^2) / (12^2) = 1/144

   Step 3: Cube (1/6): (1/6)^3 = (1^3) / (6^3) = 1/216

   Step 4: Multiply the squared result by the cubed result: (1/144) * (1/216) = 1/31104

So, the final results are:

1. 8/11
2. 54/133
3. 145/208
4. 1/31104