Explanation:

Given data: (\frac{2}{3})^2(

3

2

)

2

÷ (\frac{4}{5})^3(

5

4

)

3

× (\frac{3}{5})^2(

5

3

)

2

To find: Simplify the given equation

Solution:

According to the mathematic rule division will be done first and next will be multiplication.

(\frac{2}{3} X \frac{2}{3} )(

3

2

X

3

2

) ÷ (\frac{4}{5} X \frac{4}{5} X \frac{4}{5} )(

5

4

X

5

4

X

5

4

) × (\frac{3}{5} X \frac{3}{5} ) =(

5

3

X

5

3

)= \frac{4}{9}

9

4

÷ \frac{64}{125}

125

64

× \frac{9}{25}

25

9

Dividing the first 2 fraction we get,

\frac{4}{9}

9

4

× \frac{125}{64} = \frac{1}{9}

64

125

=

9

1

× \frac{125}{16}

16

125

Multiplying the 3 fractions \frac{1}{9}

9

1

× \frac{125}{16}

16

125

× \frac{9}{25} =\frac{5}{16}

25

9

=

16

5

.

Hence the simplification of given number is \frac{5}{16}

16

5

or 5(\frac{1}{2} )^45(

2

1

)

4

( 2^4=162

4

=16 ).