Đáp án:

$a)22\\ b)\dfrac{13}{4}\\ c)\dfrac{-599}{144}\\ d)-\dfrac{14}{45}\\ e)\dfrac{116}{35}$

Giải thích các bước giải:

$a)10.\sqrt{0,01}.\sqrt{\dfrac{16}{9}}+3\sqrt{49}-\dfrac{1}{6}\sqrt{4}\\ =10.\sqrt{\dfrac{1}{100}}.\sqrt{\dfrac{4^2}{3^2}}+3\sqrt{7^2}-\dfrac{1}{6}\sqrt{2^2}\\ =10.\dfrac{1}{10}.\dfrac{4}{3}+3.7-\dfrac{1}{6}.2\\ =\dfrac{4}{3}+21-\dfrac{1}{3}\\ =\dfrac{4}{3}-\dfrac{1}{3}+21\\ =1+21\\ =22\\ b)\left(\dfrac{5}{2}-\dfrac{4}{3}\right).\dfrac{6}{7}+\left(-\dfrac{3}{2}\right)^5:\left(-\dfrac{3}{2}\right)^3\\ =\left(\dfrac{15}{6}-\dfrac{8}{6}\right).\dfrac{6}{7}+\left(-\dfrac{3}{2}\right)^{5-3}\\ =\dfrac{7}{6}.\dfrac{6}{7}+\left(-\dfrac{3}{2}\right)^{2}\\ =1+\dfrac{9}{4}\\ =\dfrac{4}{4}+\dfrac{9}{4}\\ =\dfrac{13}{4}\\ c)\left(-\dfrac{3}{4}\right)^2+\left|-\dfrac{5}{18}\right|-\dfrac{5}{12}.\sqrt{144}\\ =\dfrac{9}{16}+\dfrac{5}{18}-\dfrac{5}{12}.\sqrt{12^2}\\ =\dfrac{9}{16}+\dfrac{5}{18}-\dfrac{5}{12}.12\\ =\dfrac{9}{16}+\dfrac{5}{18}-5\\ =\dfrac{9.9}{16.9}+\dfrac{5.8}{18.8}-\dfrac{5.144}{144}\\ =\dfrac{81}{144}+\dfrac{40}{144}-\dfrac{720}{144}\\ =\dfrac{-599}{144}\\ d)-\dfrac{7}{6}\left[\dfrac{6}{35}-\left(-\dfrac{2}{21}\right)\right]\\ =-\dfrac{7}{6}\left[\dfrac{6}{35}+\dfrac{2}{21}\right]\\ =-\dfrac{7}{6}\left[\dfrac{6.3}{35.3}+\dfrac{2.5}{21.5}\right]\\ =-\dfrac{7}{6}\left[\dfrac{18}{105}+\dfrac{10}{105}\right]\\ =-\dfrac{7}{6}.\dfrac{28}{105}\\ =-\dfrac{7}{6}.\dfrac{4}{15}\\ =-\dfrac{28}{90}\\ =-\dfrac{14}{45}\\ e)\dfrac{3}{5}-\dfrac{1}{2}\left(6-1\dfrac{3}{7}\right)+\sqrt{16+9}\\ =\dfrac{3}{5}-\dfrac{1}{2}\left(6-\dfrac{7+3}{7}\right)+\sqrt{25}\\ =\dfrac{3}{5}-\dfrac{1}{2}\left(6-\dfrac{10}{7}\right)+5\\ =\dfrac{3}{5}-\dfrac{1}{2}\left(\dfrac{42}{7}-\dfrac{10}{7}\right)+5\\ =\dfrac{3}{5}-\dfrac{1}{2}.\dfrac{32}{7}+5\\ =\dfrac{3}{5}-\dfrac{16}{7}+5\\ =\dfrac{3.7}{35}-\dfrac{16.5}{35}+\dfrac{5.35}{35}\\ =\dfrac{21}{35}-\dfrac{80}{35}+\dfrac{175}{35}\\ =\dfrac{116}{35}$

Đáp án:

`a) 22`

`b)` `9/25`

`c)` `-599/144`

`d)` `-14/45`

`e)` `(116)/35`

Giải thích các bước giải:

Bài 5:

`a)` `10*\sqrt{0,01}*\sqrt{\frac{16}{9}}+3*\sqrt{49}-1/6*\sqrt{4}`

`=10*0,1*4/3+3*7-1/6*2`

`=1*4/3+21-2/6`

`=4/3+21-1/3`

`=(4/3-1/3)+21`

`=1+21`

`=22`

`b)` `(5/2-4/3)*6/7+(-3/2)^5:(-3/2)^3`

`=(15-8)/(6)*6/7+(-3/5)^(5-3)`

`=7/6*6/7+(-3/5)^2`

`=1+(-3)^2/5^2`

`=9/25`

`c)` `(-3/4)^2+|-5/18|-5/12*\sqrt{144}`

`=9/16+5/18-5/12*12`

`=9/16+5/18-5`

`=(81+40-720)/(2*8*9)`

`=(-599)/144)`

`d)` `-7/6*[6/35-(-2/21)]`

`=-7/6*(6/35+2/21)`

`=-(7/6*6/35+7/6*2/21)`

`=-(1/5+(1)/(3*3))`

`=-(9+5)/(3*3*5)`

`=-14/45`

`e)` `3/5-1/2*(6-1 3/7)+\sqrt{16+9}`

`=3/5-1/2*(5-3/7)+\sqrt{25}`

`=3/5-1/2*32/7+5`

`=3/5-16/7+5`

`=(21-80+175)/(5*7)`

`=(116)/35`