Given:
The given expression is:
[tex]\dfrac{-2}{3}\times \dfrac{5}{7}\times \dfrac{-9}{16}\times \dfrac{14}{25}[/tex]
To find:
The value of the given expression.
Solution:
We have,
[tex]\dfrac{-2}{3}\times \dfrac{5}{7}\times \dfrac{-9}{16}\times \dfrac{14}{25}[/tex]
It can be written as:
[tex]=\dfrac{-2}{3}\times \dfrac{5}{7}\times \dfrac{-3\times 3}{2\times 2\times 2\times 2}\times \dfrac{2\times 7}{5\times 5}[/tex]
[tex]=\dfrac{-2\times 5\times (-3)\times 3\times 2\times 7}{3\times 7\times 2\times 2\times 2\times 2\times 5\times 5}[/tex]
Cancel out the common factors.
[tex]=\dfrac{-(-3)}{2\times 2\times 5}[/tex]
[tex]=\dfrac{3}{20}[/tex]
Therefore, the value of given expression is [tex]\dfrac{3}{20}[/tex].
