1; (\(\dfrac{3}{4}\))². 4² - (\(\dfrac{1}{2}\))² : 2 - 2\(\dfrac{3}{4}\)

= \(\dfrac{3^2}{4^2}\).4² - \(\dfrac{1}{4}\) : 2 - 2\(\dfrac{3}{4}\)

= 9 - \(\dfrac{1}{8}\) - \(\dfrac{11}{4}\)

= \(\dfrac{72}{8}\)  - \(\dfrac{1}{8}-\dfrac{22}{8}\)

= \(\dfrac{71}{8}\) - \(\dfrac{22}{8}\)

= \(\dfrac{49}{8}\)

2; (\(\dfrac{3}{5}\))².5² - (2\(\dfrac{1}{4}\))³ : (\(\dfrac{3}{4}\))³ - 3

 =   \(\dfrac{9}{5^2}\).5² - (\(\dfrac{9}{4}\))³ : (\(\dfrac{3}{4}\))³ - 3

= 9 - (\(\dfrac{9}{4}\) : \(\dfrac{3}{4}\))³ - 3

= 9 - 3³ - 3

= 9 - 27 - 3

= 9 - (27 + 3)

= 9 - 30

= - 21

3; 25.(\(\dfrac{-1}{5}\))³ + \(\dfrac{1}{5}\) - 2.(\(\dfrac{-1}{2}\))² - \(\dfrac{1}{2}\)

= 25.\(\dfrac{-1}{125}\) + \(\dfrac{1}{5}\) - 2.\(\dfrac{1}{4}\) - \(\dfrac{1}{2}\)

= -\(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{2}\) - \(\dfrac{1}{2}\)

 = 0 - \(\dfrac{1}{2}\) - \(\dfrac{1}{2}\)

= - \(\dfrac{1}{2}\) - \(\dfrac{1}{2}\)

= -1

4;  4.(\(\dfrac{1}{2}\))³ + 3.(\(\dfrac{1}{2}\))² - 2.(\(\dfrac{1}{2}\))⁰

=  4.\(\dfrac{1}{8}\) + 3.\(\dfrac{1}{4}\) - 2

= \(\dfrac{1}{2}\) + \(\dfrac{3}{4}\) - 2

=  \(\dfrac{5}{4}\) - 2

= - \(\dfrac{3}{4}\)

5; (- \(\dfrac{1}{2}\))².4 + \(\dfrac{1}{3}\).3² + (\(\dfrac{1}{2020}\))⁰

= \(\dfrac{1}{4}\).4 + \(3\) + 1

= 1 + 3 + 1

= 4 + 1

= 5

6; 5.(\(\dfrac{-2}{5}\))² + 2.(\(\dfrac{-2}{5}\)) + 4.(\(\dfrac{-15}{7}\))⁰

= 5.\(\dfrac{4}{5^2}\)  - \(\dfrac{4}{5}\) + 4.1

= \(\dfrac{4}{5}\) - \(\dfrac{4}{5}\) + 4

= 0 + 4

= 4

7; 3. (\(\dfrac{-2}{3}\))² - 2.(\(\dfrac{-2}{3}\)) + 4.(\(\dfrac{-2}{3}\))⁰

= \(\dfrac{4}{3}\) + \(\dfrac{4}{3}\) + 4.1

= \(\dfrac{8}{3}\) + 4

= \(\dfrac{20}{3}\)

8; 9.(\(\dfrac{2}{3}\) )² + 2.(\(\dfrac{-9}{2}\)) + 4.(\(-\dfrac{15}{7}\))⁰

  = 9.\(\dfrac{4}{9}\)  - 9 + 4.1

= 4 - 9 + 4

= -5 + 4

= - 1

9; (\(\dfrac{2}{3}\))³ - 4.(-1\(\dfrac{3}{4}\))² + (- \(\dfrac{2}{3}\))³

 = [(\(\dfrac{2}{3}\))³ + (-\(\dfrac{2}{3}\))³] - 4.(-\(\dfrac{7}{4}\))²

= [(\(\dfrac{2}{3}\))³ - (\(\dfrac{2}{3}\))³] - \(\dfrac{49}{4}\)

= 0 - \(\dfrac{49}{4}\)

= - \(\dfrac{49}{4}\)

10; (\(\dfrac{-1}{3}\))^-1 - (\(\dfrac{-6}{7}\))⁰ + (\(\dfrac{1}{2}\))² : 2

=   - 3 - 1 + \(\dfrac{1}{8}\)

= -4 + \(\dfrac{1}{8}\)

= - \(\dfrac{31}{8}\)

11; 25.(\(\dfrac{-1}{5}\))² + \(\dfrac{1}{5}\) - 9.(\(\dfrac{-1}{9}\))² + \(\dfrac{1^{20}}{9}\)

 = 1 + \(\dfrac{1}{5}\) - \(\dfrac{1}{9}\) + \(\dfrac{1}{9}\)

= \(\dfrac{6}{5}\) + (-\(\dfrac{1}{9}\) + \(\dfrac{1}{9}\))

= \(\dfrac{6}{5}\) + 0

= \(\dfrac{6}{5}\) 

12; (-\(\dfrac{1}{3}\))² + (-\(\dfrac{1}{4}\))³.64 + ( - \(\dfrac{2015}{2016}\))⁰

 =  \(\dfrac{1}{9}\) - 1 + 1

= \(\dfrac{1}{9}\) + (-1 + 1)

= \(\dfrac{1}{9}\) + 0

= \(\dfrac{1}{9}\) 

13; \(\dfrac{1}{3}\) - \(\dfrac{1}{3}\) : (-\(\dfrac{2}{3}\))² + (-3)³.(7\(\dfrac{7}{9}\) - 9\(\dfrac{2}{3}\))

  = \(\dfrac{1}{3}\)  -  \(\dfrac{3}{4}\) - 27.(\(\dfrac{70}{9}\) - \(\dfrac{29}{3}\))

=   ( \(\dfrac{1}{3}\) - \(\dfrac{3}{4}\)) - 27.(-\(\dfrac{17}{9}\))

= -\(\dfrac{5}{12}\) + 51

= \(\dfrac{607}{12}\)