Question

(2/3)²:(4/9)²=(2/7×5/12:5/14)²=​

Answer 1

вот, надеюсь помогла))))

Answer 2

To simplify the expression (2/3)²:(4/9)², you can follow these steps:

Step 1: Square each of the fractions inside the parentheses: (2/3)² = (2²)/(3²) = 4/9 (4/9)² = (4²)/(9²) = 16/81

Step 2: Divide the results of the squared fractions: (4/9) / (16/81) = (4/9) * (81/16)

Step 3: Simplify the multiplication by multiplying the numerators and denominators: (4 * 81) / (9 * 16) = 324 / 144

Step 4: Simplify further by finding the greatest common divisor (GCD) of 324 and 144, which is 36, and divide both the numerator and denominator by 36: (324/36) / (144/36) = 9/4

So, (2/3)²:(4/9)² = 9/4.

Now, let's simplify the expression (2/7 * 5/12)²:(5/14)²:

Step 1: Multiply the fractions inside the parentheses: (2/7 * 5/12) = (10/84)

Step 2: Square the result: (10/84)² = (10/84) * (10/84)

Step 3: Simplify the multiplication by multiplying the numerators and denominators: (10 * 10) / (84 * 84) = 100 / 7056

Now, let's simplify further:

Step 4: Find the greatest common divisor (GCD) of 100 and 7056, which is 4, and divide both the numerator and denominator by 4: (100/4) / (7056/4) = 25 / 1764

So, (2/7 * 5/12)²:(5/14)² = 25/1764.

In summary: (2/3)²:(4/9)² = 9/4 (2/7 * 5/12)²:(5/14)² = 25/1764