\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)\times\left(1,25\times0,36-3,75\times0,12\right)\)

\(=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)\times\left(1,25\times0,36-1,25\times3\times0,12\right)\)

\(=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)\times\left(1,25\times0,36-1,25\times0,36\right)\)

\(=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)\times0\)

\(=0\)

( 1/2 + 1/4 + 1/6 + 1/8 + 1/10 ) × ( 1,25 × 0,36 - 3,75 × 0,12 )

= ( 1/2 + 1/4 + 1/6 + 1/8 + 1/10 ) × 0 

(3,75 : 1,25 = 3 ; 0,36 : 0,12 = 3 )

= 0

\(\sqrt{0,36}-\left|-0,75\right|:\left(-1\dfrac{3}{4}\right)\\ =0,6-0,75:\dfrac{-7}{4}\\ =\dfrac{3}{5}-\dfrac{3}{4}\cdot\dfrac{-4}{7}\\ =\dfrac{3}{5}-\dfrac{-12}{28}\\ =\dfrac{3}{5}+\dfrac{3}{7}\\ =\dfrac{36}{35}\)

\(1-\left(\dfrac{5}{9}-\dfrac{2}{3}\right)^2:\dfrac{4}{27}\\ =1-\left(\dfrac{5}{9}-\dfrac{6}{9}\right)^2\cdot\dfrac{27}{4}\\ =1-\left(-\dfrac{1}{9}\right)^2\cdot\dfrac{27}{4}\\ =1-\dfrac{1}{81}\cdot\dfrac{27}{4}\\ =1-\dfrac{1}{12}\\ =\dfrac{11}{12}\)

1/9 - 0,3 . 5/9 + 1/3 + 5

= 1/9 - 3/10 . 5/9 + 1/3 + 5

= 1/9 - 1/6 + 16/3

= -1/18 + 16/3

= 95/18

a: \(=\left(1.25\right)^{16}\cdot8^{16}\cdot8=8\cdot10^{16}\)

b: \(=\left(\dfrac{5}{2}\right)^{13}\cdot4^{13}\cdot4^2=10^{13}\cdot4^2\)

c: \(=\left(0.25\right)^4\cdot8^4\cdot8^2=2^4\cdot8^2=64\cdot16=1024\)

d: \(=\left(\dfrac{1}{2}\right)^{15}\cdot2^{18}=2^3=8\)

e: \(=\left(\dfrac{1}{3}\cdot6\right)^7\cdot\left(\dfrac{1}{2}\right)^7\cdot\dfrac{1}{2}=2^7\cdot\left(\dfrac{1}{2}\right)^7\cdot\dfrac{1}{2}=\dfrac{1}{2}\)

a)\({\left( {\frac{2}{5} + \frac{1}{2}} \right)^2} = {\left( {\frac{4}{{10}} + \frac{5}{{10}}} \right)^2} = {\left( {\frac{9}{{10}}} \right)^2} = \frac{{81}}{{100}}\);               

 b)\({\left( {0,75 - 1\frac{1}{2}} \right)^3} = {\left( {\frac{3}{4} - \frac{3}{2}} \right)^3} = {\left( {\frac{3}{4} - \frac{6}{4}} \right)^3} = {\left( { - \frac{3}{4}} \right)^3} = \frac{{ - 27}}{{64}};\)

c)

\(\begin{array}{l}{\left( {\frac{3}{5}} \right)^{15}}:{\left( {0,36} \right)^5} = {\left( {\frac{3}{5}} \right)^{15}}:{\left( {\frac{9}{{25}}} \right)^5}\\ = {\left( {\frac{3}{5}} \right)^{15}}:{\left[ {{{\left( {\frac{3}{5}} \right)}^2}} \right]^5} = {\left( {\frac{3}{5}} \right)^{15}}:{\left( {\frac{3}{5}} \right)^{10}} = {\left( {\frac{3}{5}} \right)^5}\end{array}\)

d) \({\left( {1 - \frac{1}{3}} \right)^8}:{\left( {\frac{4}{9}} \right)^3} = {\left( {\frac{3}{3} - \frac{1}{3}} \right)^8}:{\left( ({\frac{2}{3}})^2 \right)^3}\\= {\left( {\frac{2}{3}} \right)^8}:{\left( {\frac{2}{3}} \right)^6} = {\left( {\frac{2}{3}} \right)^{8-6}}\\= {\left( {\frac{2}{3}} \right)^2} = \frac{4}{9}\)

a: =6-6=0

b: \(=\dfrac{-5}{4}:\dfrac{2-7}{8}+\dfrac{3}{2}\cdot\dfrac{2-5}{6}\)

\(=\dfrac{-5}{4}\cdot\dfrac{8}{-5}+\dfrac{3}{2}\cdot\dfrac{-3}{6}\)

\(=2+\dfrac{-9}{12}=2-\dfrac{3}{4}=\dfrac{5}{4}\)

c: \(=2,5\cdot\left(-0,65\right)+1,5\left(-0,3-0,35\right)=-0,65\cdot4=-2,6\)

a) 2023 – 106,5 : 2,5 +2,5   

=2023-42,6+2,5

=1980,4+2,5

=1982,9

b) 0,36 × 950 + 0,18 × 726 × 2 + 3 × 324 × 0,12

= 0,36 × 950 + 0,36 × 726 + 0,36 × 324

= 0,36 × (950 + 726 + 324)

= 0,36 × 2000

= 0,36 × 2 × 1000

= 0,72 × 1000

= 720