`1//([-1]/2)^2 . |+8|-(-1/2)^3:|-1/16|=1/4 .8+1/8 .16=2+2=4`

`2//|-0,25|-(-3/2)^2:1/4+3/4 .2017^0=0,25-2,25.4+0,75.1=0,25-9+0,75=-8,75+0,75-8`

`3//|2/3-5/6|.(3,6:2 2/5)^3=|-1/6|.(3/2)^3=1/6 . 27/8=9/16`

`4//|(-0,5)^2+7/2|.10-(29/30-7/15):(-2017/2018)^0=|1/4+7/2|.10-1/2:1=|15/4|.10-1/2=15/4 .10-1/2=75/2-1/2=37`

`5// 8/3+(3-1/2)^2-|[-7]/3|=8/3+(5/2)^2-7/3=8/3+25/4-7/3=107/12-7/3=79/12`

e: \(=\left(\dfrac{18}{37}+\dfrac{19}{37}\right)+\left(\dfrac{8}{24}+\dfrac{2}{3}\right)-\dfrac{47}{24}=2-\dfrac{47}{24}=\dfrac{1}{24}\)

f: \(=-8\cdot\dfrac{1}{2}:\left(\dfrac{9}{4}-\dfrac{7}{6}\right)\)

\(=-4:\dfrac{13}{12}=\dfrac{-48}{13}\)

g: \(=\dfrac{4}{25}+\dfrac{11}{2}\cdot\dfrac{5}{2}-\dfrac{8}{4}=\dfrac{4}{25}+\dfrac{55}{4}-2=\dfrac{1191}{100}\)

\(D=\left(-8\right).\left(\dfrac{3}{4}-\dfrac{1}{4}\right):\left(\dfrac{9}{4}-\dfrac{7}{6}\right)=\left(-8\right)\dfrac{1}{2}:\dfrac{13}{12}=\left(-4\right).\dfrac{12}{13}=-\dfrac{48}{13}\)

\(\text{A=}\left(\dfrac{7}{8}-0,25\right):\left(\dfrac{5}{6}-0,75\right)^2\)

\(A=\left(\dfrac{7}{8}-\dfrac{1}{4}\right):\left(\dfrac{5}{6}-\dfrac{3}{4}\right)^2\)

\(A=\left(\dfrac{7}{8}+\dfrac{-1}{4}\right):\dfrac{1}{144}\)

\(A=\dfrac{5}{8}.144=90\)

\(\text{B=}\dfrac{3}{4}.1\dfrac{4}{9}-\left(\dfrac{-3}{4}\right)\)

\(B=\dfrac{3}{4}.\dfrac{13}{9}+\dfrac{3}{4}\)

\(B=\dfrac{13}{12}+\dfrac{3}{4}\)

\(B=\dfrac{11}{6}\)

a: \(=\dfrac{9}{13}\cdot\dfrac{4}{5}=\dfrac{36}{65}\)

b: \(=\dfrac{-7}{10}:\dfrac{3}{2}=\dfrac{-7}{10}\cdot\dfrac{2}{3}=\dfrac{-14}{30}=-\dfrac{7}{15}\)

c: \(=\dfrac{7}{6}\left(3+\dfrac{1}{4}-\dfrac{1}{4}\right)=\dfrac{7}{6}\cdot3=\dfrac{7}{2}\)

\(N=4\cdot16\cdot\dfrac{9}{16}\cdot\dfrac{4}{5}\cdot\dfrac{27}{8}=4\cdot9\cdot\dfrac{4}{5}\cdot\dfrac{27}{8}\)

\(=\dfrac{16}{5}\cdot\dfrac{243}{8}=\dfrac{486}{5}\)

a) \(\left(\dfrac{1}{16}\right)^{-\dfrac{3}{4}}+810000^{0.25}-\left(7\dfrac{19}{32}\right)^{\dfrac{1}{5}}\)

\(=\left(\dfrac{1}{2}\right)^{4.\left(-\dfrac{3}{4}\right)}+\left(30\right)^{4.0,25}-\left(\dfrac{243}{32}\right)^{\dfrac{1}{5}}\)

\(=\left(\dfrac{1}{2}\right)^{-3}+30-\left(\dfrac{3}{2}\right)^{5.\dfrac{1}{5}}\)

\(=2^3+30-\dfrac{3}{2}\)

\(=36,5\)

b) \(=\left(0,1\right)^{3.\left(-\dfrac{1}{3}\right)}-2^{-2}.2^{6.\dfrac{2}{3}}-\left[\left(2\right)^3\right]^{-\dfrac{4}{3}}\)

\(=0,1^{-1}-2^2-2^{-4}\)

\(=10-4-\dfrac{1}{16}\)

\(=\dfrac{95}{16}\)

c) \(=3^{3.\dfrac{2}{3}}-\dfrac{1}{\left(-2\right)^2}+\left(\dfrac{27}{8}\right)^{-\dfrac{1}{3}}\)

\(=9-\dfrac{1}{4}+\left(\dfrac{3}{2}\right)^{3.\dfrac{-1}{3}}\)

\(=9-\dfrac{1}{4}+\left(\dfrac{3}{2}\right)^{-1}\)

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

\(=\dfrac{113}{12}\)

\(A=4.\dfrac{25}{16}+25.\left[\dfrac{9}{16}:\dfrac{125}{64}\right]:\dfrac{-27}{8}\)

\(=\dfrac{25}{16}+25.\dfrac{36}{125}:\dfrac{-27}{8}=-\dfrac{137}{240}\left(1\right)\)

\(B=125.\left[\dfrac{1}{25}+\dfrac{1}{64}:8\right]-64.\dfrac{1}{64}\)

\(=125.\dfrac{89}{1600}:8-64.\dfrac{1}{64}=\dfrac{-67}{512}\left(2\right)\)

Vì (2) > (1) => B > A

Ta lần lượt có:

\(\dfrac{1}{0,25}=\dfrac{100}{25}=4;\) \(\left(1\dfrac{1}{4}\right)^2=\left(\dfrac{5}{4}\right)^2=\dfrac{25}{16};\)

\(\dfrac{1}{\left(\dfrac{4}{3}\right)^2}=\dfrac{1}{\dfrac{16}{9}}=\dfrac{9}{16};\) \(\left(\dfrac{5}{4}\right)^3=\dfrac{125}{64}\) và \(\dfrac{1}{\left(-\dfrac{2}{3}\right)^3}=\dfrac{1}{-\dfrac{8}{27}}=-\dfrac{27}{8}\)

Vậy \(P=4.\dfrac{25}{16}+25.\left[\dfrac{9}{16}:\dfrac{125}{64}\right]:\left(-\dfrac{27}{8}\right)\)

\(=\dfrac{25}{4}-25.\dfrac{9}{16}.\dfrac{64}{125}.\dfrac{8}{27}\)

\(=\dfrac{25}{4}-\dfrac{32}{15}\)

\(=\dfrac{375-128}{60}=\dfrac{247}{60}\)

P=4.(25/16)+25.(9/16:25/16):(-27/8)

=25/4 +25.(9/25):(-27/8)

=25/4 +9:(-27/8)

=25/4 +(-8/3)

=43/12

Bai 1: \(\left(-2\right)^3.\left(\dfrac{3}{4}-0,25\right):\left(2\dfrac{1}{4}-1\dfrac{1}{6}\right)\)

\(=\left(-8\right).\left(\dfrac{3}{4}-\dfrac{1}{4}\right):\left(\dfrac{9}{4}-\dfrac{7}{6}\right)\)

\(=\left(-8\right).\dfrac{1}{2}:\left(\dfrac{27}{12}-\dfrac{14}{12}\right)\)

\(=\left(-4\right):\dfrac{13}{12}\)

\(=\left(-4\right).\dfrac{12}{13}\)

\(=\dfrac{-48}{13}\)

Bai 2:

\(a,4\dfrac{1}{3}:\dfrac{x}{4}=6:0,3\)

\(\dfrac{13}{3}:\dfrac{x}{4}=20\)

\(\dfrac{x}{4}=\dfrac{13}{3}:20\)

\(\dfrac{x}{4}=\dfrac{13}{60}\)

➩ \(x.60=4.13\) ➩ \(x.60=52\) ➩ \(x=\dfrac{13}{15}\)

Vay \(x=\dfrac{13}{15}\)

\(b,\left(2^3:4\right).2^{\left(x+1\right)}=64\)

\(\left(8:4\right).2^{x+1}=64\)

\(2.2^{x+1}=64\)

\(2^{x+1}=32\)

➩ \(2^{x+1}=2^5\) ➩ \(x+1=5\) ➩ \(x=4\)

Vay \(x=4\)