Question

А.(2/3)²*(1/4)³*(5/4)²*(3/2)³ = б.(1 1/5)²*(2 1/2)³*(2. 1/3)²*(3. 1/3)³=

Answer 1

Ответ:

А.

2/3*2/3=6/9

1/4*1/4*1/4=1/64

5/4*5/4=25/16

3/2*3/2*3/2=27/8

6/9*1/64*25/16*27/8=4050/73 728=2025/36 864

Answer 2

To simplify the given expressions, let's evaluate each expression step by step.

Expression A:

(2/3)² * (1/4)³ * (5/4)² * (3/2)³

First, let's simplify the individual fractions:

(2/3)² = 4/9

(1/4)³ = 1/64

(5/4)² = 25/16

(3/2)³ = 27/8

Now, substitute these values back into the expression:

(4/9) * (1/64) * (25/16) * (27/8)

To multiply the fractions, multiply the numerators together and the denominators together:

(4 * 1 * 25 * 27) / (9 * 64 * 16 * 8)

Simplify the numerator and denominator:

(27000) / (73728)

Expression A simplifies to 27000/73728.

Expression B:

(1 1/5)² * (2 1/2)³ * (2 1/3)² * (3 1/3)³

To simplify mixed numbers, convert them into improper fractions:

(1 1/5) = (6/5)

(2 1/2) = (5/2)

(2 1/3) = (7/3)

(3 1/3) = (10/3)

Now, substitute these values back into the expression:

(6/5)² * (5/2)³ * (7/3)² * (10/3)³

Simplify the fractions:

(36/25) * (125/8) * (49/9) * (1000/27)

Multiply the numerators together and the denominators together:

(36 * 125 * 49 * 1000) / (25 * 8 * 9 * 27)

Simplify the numerator and denominator:

(1102500000) / (48600)

Expression B simplifies to 1102500000/48600.

So, the simplified values are:

Expression A = 27000/73728 Expression B = 1102500000/48600