a. 84 : 4 + 3⁹ : 3⁷ + 5⁰

= 21 + 3² + 1

= 21 + 9 + 1

= 21 + 10 = 31

b. 2010 - 2000 : [ 486 - 2.(7² - 6) ]

= 2010 - 2000 : [ 486 - 2.(49 - 6) ]

= 2010 - 2000 : ( 486 - 2.43 )

= 2010 - 2000 : ( 486 - 86 )

= 2010 - 2000 : 400

= 2010 - 5

= 2005

c. 6² - 120 + (-5) - |-5|

= 36 - 120 - 5 - 5

= 36 - 

\(\left(5^{19}\cdot5^{14}\right):5^{32}\)

\(=5^{19+14}:5^{32}\)

\(=5^{33}:5^{32}\)

\(=5^{33-32}\)

\(=5\)

\(\left(\sqrt{10}-\sqrt{2}\right)\sqrt{4+\sqrt{6-2\sqrt{5}}}\\ =\left(\sqrt{10}-\sqrt{2}\right)\sqrt{4+\sqrt{\left(\sqrt{5}-1\right)^2}}\\ =\left(\sqrt{10}-\sqrt{2}\right)\sqrt{3+\sqrt{5}}\\ =\sqrt{10}\cdot\sqrt{3+\sqrt{5}}-\sqrt{2}\cdot\sqrt{3+\sqrt{5}}\\ =\sqrt{30+10\sqrt{5}}-\sqrt{6+2\sqrt{5}}\\ =\sqrt{\left(5+\sqrt{5}\right)^2}-\sqrt{\left(\sqrt{5}+1\right)^2}\\ =5+\sqrt{5}-\sqrt{5}-1\\ =4\)

\(\dfrac{-8}{3}\)

a: \(=12\sqrt{80}=48\sqrt{5}\)

b: \(=2\sqrt{5}\cdot2\sqrt{3}-10=4\sqrt{15}-10\)

c: =20-9=11

a, \(\dfrac{3}{5}\). (\(-\dfrac{9}{11}\)) + \(\dfrac{-3}{5}\).\(\dfrac{2}{11}\) + \(\dfrac{3}{5}\)

= \(\dfrac{3}{5}\).( - \(\dfrac{9}{11}\) - \(\dfrac{2}{11}\) + 1)

= \(\dfrac{3}{5}\).(- \(\dfrac{11}{11}\) + 1)

= \(\dfrac{3}{5}\).(1-1)

= \(\dfrac{3}{5}\).0

= 0