Ex 5 e 6

(1 / 12^2 * 10^2 * 9^2/5^2) : 5/2

(100/144*81/25) * 2/5

9/4*2/5 

18/20

9/10

(1/3 - 1/4)^2·10^2·(1 + 4/5)^2/(2 + 1/2)=

=(1/12)^2·10^2·(9/5)^2/(5/2)=

=1/144·100·(81/25)/(5/2)=

=9/4/(5/2)= 9/10

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(3 - 3/2)^2·(1/5 + (1/2 + 1)^2·(1 - 11/27))/(23/10)=

=(3/2)^2·(1/5 + (3/2)^2·(16/27))/(23/10)=

=9/4·(1/5 + 9/4·(16/27))/(23/10)=

=9/4·(1/5 + 4/3)/(23/10)=

=9/4·(23/15)/(23/10)=

=69/20/(23/10) = 3/2

3^2/2^2 * (1/5 + 3^2/2^2 * 16/27) * 10/23

9/4 * (1/5 + 4/3) * 10/23

9/4 * (3+20) / 15 *10/23

9/4 * 2/3

18/12

3/2

============================================================

$\small  \left[\left(\dfrac{1}{3}-\dfrac{1}{4}\right)^2×10^2×\left(1+\dfrac{4}{5}\right)^2\right]÷\left(2+\dfrac{1}{2}\right) =$

$\small = \left[\left(\dfrac{4-3}{12}\right)^2×100×\left(\dfrac{5+4}{5}\right)^2\right]÷\left(\dfrac{4+1}{2}\right) =$

$\small = \left[\left(\dfrac{1}{12}\right)^2×100×\left(\dfrac{9}{5}\right)^2\right]÷\dfrac{5}{2} =$

$\small = \left[\dfrac{1}{144}×\cancel{100}^4×\dfrac{81}{\cancel{25}_1}\right]×\dfrac{2}{5} =$

$\small = \left[\dfrac{1}{144}×4×\dfrac{81}{1}\right]×\dfrac{2}{5} =$

$\small = \left[\dfrac{1}{\cancel{144}_{36}}×\cancel4^1×\dfrac{81}{1}\right]×\dfrac{2}{5} =$

$\small = \left[\dfrac{1}{\cancel{36}_4}×\dfrac{\cancel{81}^9}{1}\right]×\dfrac{2}{5} =$

$\small = \left[\dfrac{1}{4}×\dfrac{9}{1}\right]×\dfrac{2}{5} =$

$\small = \dfrac{9}{\cancel4_2}×\dfrac{\cancel2^1}{5} =$

$\small = \dfrac{9}{2}×\dfrac{1}{5} =$

$\small = \dfrac{9}{10}$

=========================================================

$\small  \left(3- \dfrac{3}{2}\right)^2×\left[\dfrac{1}{5}+\left(\dfrac{1}{2}+1\right)^2×\left(1-\dfrac{11}{27}\right)\right]÷\dfrac{23}{10} =$

$\small = \left( \dfrac{6-3}{2}\right)^2×\left[\dfrac{1}{5}+\left(\dfrac{1+2}{2}\right)^2×\left(\dfrac{27-11}{27}\right)\right]×\dfrac{10}{23} =$

$\small = \left( \dfrac{3}{2}\right)^2×\left[\dfrac{1}{5}+\left(\dfrac{3}{2}\right)^2×\dfrac{16}{27}\right]×\dfrac{10}{23} =$

$\small = \dfrac{9}{4}×\left[\dfrac{1}{5}+\dfrac{\cancel9^1}{\cancel4_1}×\dfrac{\cancel{16}^4}{\cancel{27}_3}\right]×\dfrac{10}{23} =$

$\small = \dfrac{9}{4}×\left[\dfrac{1}{5}+\dfrac{1}{1}×\dfrac{4}{3}\right]×\dfrac{10}{23} =$

$\small = \dfrac{9}{4}×\left[\dfrac{1}{5}+\dfrac{4}{3}\right]×\dfrac{10}{23} =$

$\small = \dfrac{9}{4}×\left[\dfrac{3+20}{15}\right]×\dfrac{10}{23} =$

$\small = \dfrac{9}{4}×\dfrac{\cancel{23}^1}{\cancel{15}_3}×\dfrac{\cancel{10}^2}{\cancel{23}_1} =$

$\small = \dfrac{9}{4}×\dfrac{1}{3}×\dfrac{2}{1} =$

$\small = \dfrac{\cancel9^3}{\cancel4_2}×\dfrac{1}{\cancel3_1}×\dfrac{\cancel2^1}{1} =$

$\small = \dfrac{3}{2}×\dfrac{1}{1}×\dfrac{1}{1} =$

$\small = \dfrac{3}{2}$