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$c)$
$2\dfrac{1}{3} - 1{,}5 \cdot \left(\dfrac{4}{3}\right)^2$
$= \dfrac{7}{3} - \dfrac{3}{2} \cdot \dfrac{16}{9}$
$= \dfrac{7}{3} - \dfrac{3 \cdot 16}{2 \cdot 9}$
$= \dfrac{7}{3} - \dfrac{48}{18}$
$= \dfrac{7}{3} - \dfrac{8}{3}$
$= \dfrac{-1}{3}$
$d)$
$\dfrac{-5}{6} \cdot \dfrac{7}{4} + \dfrac{-5}{6} \cdot \dfrac{7}{3}$
$= \dfrac{-5}{6} \cdot \left(\dfrac{7}{4} + \dfrac{7}{3}\right)$
$= \dfrac{-5}{6} \cdot \left(\dfrac{21}{12} + \dfrac{28}{12}\right)$
$= \dfrac{-5}{6} \cdot \dfrac{49}{12}$
$= \dfrac{-245}{72}$
$e)$
$\dfrac{-4}{7} \cdot \dfrac{3}{11} - \dfrac{4}{7} : \dfrac{11}{8}$
$= \dfrac{-4}{7} \cdot \dfrac{3}{11} - \dfrac{4}{7} \cdot \dfrac{8}{11}$
$= \dfrac{-4}{7} \cdot \left(\dfrac{3}{11} + \dfrac{8}{11}\right)$
$= \dfrac{-4}{7} \cdot \dfrac{11}{11}$
$= \dfrac{-4}{7} \cdot 1$
$= \dfrac{-4}{7}$
$f)$
$3^3 - 2 \cdot \left(\dfrac{1}{2}\right)^0 + 9 \cdot \sqrt{\dfrac{1}{9}} - \dfrac{4}{3} \cdot |-3|$
$= 27 - 2 \cdot 1 + 9 \cdot \dfrac{1}{3} - \dfrac{4}{3} \cdot 3$
$= 27 - 2 + 3 - 4$
$= 25 + 3 - 4$
$= 28 - 4$
$= 24$
$g)$
$\dfrac{6}{5} : \left[0{,}3 - 4 \cdot \left(\dfrac{1}{8} + \left(\dfrac{1}{5} - \dfrac{3}{8}\right)\right)\right]$
$= \dfrac{6}{5} : \left[\dfrac{3}{10} - 4 \cdot \left(\dfrac{1}{5} + \dfrac{1}{8} - \dfrac{3}{8}\right)\right]$
$= \dfrac{6}{5} : \left[\dfrac{3}{10} - 4 \cdot \left(\dfrac{1}{5} - \dfrac{2}{8}\right)\right]$
$= \dfrac{6}{5} : \left[\dfrac{3}{10} - 4 \cdot \left(\dfrac{1}{5} - \dfrac{1}{4}\right)\right]$
$= \dfrac{6}{5} : \left[\dfrac{3}{10} - 4 \cdot \left(\dfrac{4}{20} - \dfrac{5}{20}\right)\right]$
$= \dfrac{6}{5} : \left[\dfrac{3}{10} - 4 \cdot \left(\dfrac{-1}{20}\right)\right]$
$= \dfrac{6}{5} : \left[\dfrac{3}{10} + \dfrac{4}{20}\right]$
$= \dfrac{6}{5} : \left[\dfrac{3}{10} + \dfrac{2}{10}\right]$
$= \dfrac{6}{5} : \dfrac{5}{10}$
$= \dfrac{6}{5} : \dfrac{1}{2}$
$= \dfrac{6}{5} \cdot 2$
$= \dfrac{12}{5}$
$h)$
$\sqrt{\dfrac{9}{25}} \cdot \left|\dfrac{-10}{3}\right| - \sqrt{\dfrac{1}{4}} \cdot |-1{,}2| + \left(\dfrac{-1}{2}\right)^3$
$= \dfrac{3}{5} \cdot \dfrac{10}{3} - \dfrac{1}{2} \cdot 1{,}2 + \left(\dfrac{-1}{8}\right)$
$= \dfrac{3 \cdot 10}{5 \cdot 3} - \dfrac{1}{2} \cdot \dfrac{6}{5} - \dfrac{1}{8}$
$= 2 - \dfrac{3}{5} - \dfrac{1}{8}$
$= \dfrac{80}{40} - \dfrac{24}{40} - \dfrac{5}{40}$
$= \dfrac{51}{40}$
$i)$
$\left(\dfrac{-2}{3}\right)^3 : \dfrac{4}{27} - \dfrac{1}{4} \cdot \dfrac{8}{3} + 1{,}5$
$= \dfrac{-8}{27} : \dfrac{4}{27} - \dfrac{8}{12} + \dfrac{3}{2}$
$= \dfrac{-8}{27} \cdot \dfrac{27}{4} - \dfrac{2}{3} + \dfrac{3}{2}$
$= -2 - \dfrac{2}{3} + \dfrac{3}{2}$
$= \dfrac{-12}{6} - \dfrac{4}{6} + \dfrac{9}{6}$
$= \dfrac{-7}{6}$
$\color{#FFB52E}{꧁}\color{#DAA520}{段}\color{#FFD700}{光}\color{#FFC928}{明}\color{#FFB52E}{꧂}$
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Đáp án+Giải thích các bước giải:
`c) 2 1/3-1,5. (4/3)^{2}`
`=(2+1/3)-3/2. 4/3. 4/3`
`=(6/3+1/3)-(3.2.2)/(2.3). 4/3`
`=7/3-2. 4/3`
`=7/3-8/3`
`=-1/3`
`d)(-5)/(6): 7/4+(-5)/(6): 7/3`
`=(-5/6). 4/7+(-5/6). 3/7`
`=(-5/6). (4/7+3/7)`
`=(-5/6). 7/7`
`=(-5/6).1`
`=-5/6`
`e)(-4)/(7). 3/11-4/7: 11/8`
`=4/7.(-3/11)-4/7. 8/11`
`=4/7.[(-3/11)-8/11]`
`=4/7. (-11/11)`
`=4/7. (-1)`
`=-4/7`
`f)3^{3}-2.(1/2)^{0}+9\sqrt{1/9}-4/3. |-3|`
`=27-2. 1+9\sqrt{(1/3)^{2}}-4/3. 3`
`=27-2+9. 1/3-4`
`=25-4+9/3`
`=21+3`
`=24`
`g)6/5:[0,3-4.(1/8+(1/5-3/8))]`
`=6/5:[3/10-4.(1/8+1/5-3/8)]`
`=6/5:[3/10-4.(1/5-2/8)]`
`=6/5:[3/10-4.(1/5-1/4)]`
`=6/5:[3/10-4.(4/20-5/20)]`
`=6/5:[3/10-4.(-1/20)]`
`=6/5:(3/10+4/20)`
`=6/5:(3/10+1/5)`
`=6/5:(3/10+2/10)`
`=6/5: 5/10`
`=6/5: 1/2`
`=6/5 . 2`
`=12/5`
`h)\sqrt{9/25}.|-10/3|-\sqrt{1/4}.|-1,2|+((-1)/(2))^{3}`
`=\sqrt{(3/5)^{2}}. [-(-10/3)]-\sqrt{(1/2)^{2}}.[-(-1,2)]+(-1/8)`
`=3/5. 10/3-1/2. 1,2-1/8`
`=(3.5.2)/(5.3)-1/2. 12/10-1/8`
`=2-1/2. 6/5-1/8`
`=2-(1.2.3)/(2.5)-1/8`
`=2-3/5-1/8`
`=80/40-24/40-5/40`
`=51/40`
`i)((-2)/(3))^{3}: 4/27-1/4. 8/3+1,5`
`=(-8/27): 4/27-(1.2.4)/(4.3)+15/10`
`=-8/4-2/3+3/2`
`=-2-2/3+3/2`
`=-12/6-4/6+9/6`
`=-7/6`
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