Option D:
[tex]\left(-\frac{2}{5}\right)\left(-\frac{8}{9}\right)\left(\frac{1}{3}\right)\left(\frac{2}{7}\right)[/tex] is positive product.
Solution:
Some basic rules of product:
If the negative sign is in even number of times then the product is positive.
If the negative sign is in odd number of times then the product is negative.
To find which product is positive:
Option A:
[tex]$\left(\frac{2}{5}\right)\left(-\frac{8}{9}\right)\left(-\frac{1}{3}\right)\left(-\frac{2}{7}\right)[/tex]
Here, number of negative signs = 3 which is odd
So, the product is negative.
Option B:
[tex]$\left(-\frac{2}{5}\right)\left(\frac{8}{9}\right)\left(-\frac{1}{3}\right)\left(-\frac{2}{7}\right)[/tex]
Here, number of negative signs = 3 which is odd
So, the product is negative.
Option C:
[tex]$\left(\frac{2}{5}\right)\left(\frac{8}{9}\right)\left(\frac{1}{3}\right)\left(-\frac{2}{7}\right)[/tex]
Here, number of negative sign = 1 which is odd
So, the product is negative.
Option D:
[tex]$\left(-\frac{2}{5}\right)\left(-\frac{8}{9}\right)\left(\frac{1}{3}\right)\left(\frac{2}{7}\right)[/tex]
Here, number of negative sign = 2 which is even
So, the product is positive.
Hence option D is the correct answer.
[tex]\left(-\frac{2}{5}\right)\left(-\frac{8}{9}\right)\left(\frac{1}{3}\right)\left(\frac{2}{7}\right)[/tex] is positive product.
