Simplify and express each of the following as power of a rational number

i) $ \left(\frac{2}{3}\right)^{3} \times\left(\frac{-6}{7}\right)^{2} \times\left(\frac{-7}{4}\right) \times \frac{3}{2} $

ii) $ -\left(\frac{2}{5}\right)^{2} \times\left(\frac{5}{7}\right)^{2} \times \frac{49}{5}+\left(\frac{-4}{5}\right)^{3} \times \frac{5}{4} \times \frac{3}{4} $

1) Given:  $\left(\frac{2}{3}\right)^{3} \times \ \left(\frac{-6}{7}\right)^{2} \times \ \frac{-7}{4} \times \ \frac{3}{2}$

To find: We have to find the value of $\left(\frac{2}{3}\right)^{3} \times \ \left(\frac{-6}{7}\right)^{2} \times \ \frac{-7}{4} \times \ \frac{3}{2}$

Solution: 

$\left(\frac{2}{3}\right)^{3} \times \ \left(\frac{-6}{7}\right)^{2} \times \ \frac{-7}{4} \times \ \frac{3}{2}$

$=\ \frac{2}{3} \ \times \ \frac{2}{3} \ \times \ \frac{2}{3} \ \times \ \frac{-6}{7} \ \times \frac{-6}{7} \ \times \frac{-7}{4} \ \times \frac{3}{2} \ $

$=\ \ \frac{-2}{7} \ \times \ \frac{2}{1} \ =\ \frac{-4}{7}$

2) Given: $-\left(\frac{2}{5}\right)^{2} \times \ \left(\frac{5}{7}\right)^{2} \times \ \frac{49}{5} +\ \left(\frac{-4}{5}\right)^{3} \ \times \ \frac{5}{4} \ \times \ \frac{3}{4}$

To find: We have to find the value of $-\left(\frac{2}{5}\right)^{2} \times \ \left(\frac{5}{7}\right)^{2} \times \ \frac{49}{5} +\ \left(\frac{-4}{5}\right)^{3} \ \times \ \frac{5}{4} \ \times \ \frac{3}{4}$

Solution: $-\left(\frac{2}{5}\right)^{2} \times \ \left(\frac{5}{7}\right)^{2} \times \ \frac{49}{5} +\ \left(\frac{-4}{5}\right)^{3} \ \times \ \frac{5}{4} \ \times \ \frac{3}{4}$

 $=\ -\frac{4}{25} \ \times \ \frac{25}{49} \ \times \ \frac{49}{5} \ +\ \frac{-64}{125} \ \times \frac{5}{4} \ \times \frac{3}{4} \ $

$=\ \ \frac{-4}{5} \ +\ \frac{-12}{25} \ =\frac{-20}{25} \ +\ \frac{-12}{25} \ =\ \frac{-32}{25}$

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Updated on: 10-Oct-2022

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