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a) \({\left( {\frac{8}{9}} \right)^3} \cdot \frac{4}{3} \cdot \frac{2}{3} = {\left( {\frac{8}{9}} \right)^3}.\frac{8}{9} = {\left( {\frac{8}{9}} \right)^{3+1}}={\left( {\frac{8}{9}} \right)^4}\)
b) \({\left( {\frac{1}{4}} \right)^7} \cdot 0,25 = {\left( {0,25} \right)^7}.0,25 ={\left( {0,25} \right)^{7+1}}= {\left( {0,25} \right)^8}\)
c) \({( - 0,125)^6}:\frac{{ - 1}}{8} = {\left( {\frac{{ - 1}}{8}} \right)^6}:\frac{{ - 1}}{8} = {\left( {\frac{{ - 1}}{8}} \right)^{6-1}}= {\left( {\frac{{ - 1}}{8}} \right)^5}\)
d) \({\left[ {{{\left( {\frac{{ - 3}}{2}} \right)}^3}} \right]^2} = {\left( {\frac{{ - 3}}{2}} \right)^{3.2}} = {\left( {\frac{{ - 3}}{2}} \right)^6}\)
\(1,\\ a,=\left(\dfrac{1}{4}\right)^3\cdot32=\dfrac{1}{64}\cdot32=\dfrac{1}{2}\\ b,=\left(\dfrac{1}{8}\right)^3\cdot512=\dfrac{1}{512}\cdot512=1\\ c,=\dfrac{2^6\cdot2^{10}}{2^{20}}=\dfrac{1}{2^4}=\dfrac{1}{16}\\ d,=\dfrac{3^{44}\cdot3^{17}}{3^{30}\cdot3^{30}}=3\\ 2,\\ a,A=\left|x-\dfrac{3}{4}\right|\ge0\\ A_{min}=0\Leftrightarrow x=\dfrac{3}{4}\\ b,B=1,5+\left|2-x\right|\ge1,5\\ A_{min}=1,5\Leftrightarrow x=2\\ c,A=\left|2x-\dfrac{1}{3}\right|+107\ge107\\ A_{min}=107\Leftrightarrow2x=\dfrac{1}{3}\Leftrightarrow x=\dfrac{1}{6}\)
\(d,M=5\left|1-4x\right|-1\ge-1\\ M_{min}=-1\Leftrightarrow4x=1\Leftrightarrow x=\dfrac{1}{4}\\ 3,\\ a,C=-\left|x-2\right|\le0\\ C_{max}=0\Leftrightarrow x=2\\ b,D=1-\left|2x-3\right|\le1\\ D_{max}=1\Leftrightarrow x=\dfrac{3}{2}\\ c,D=-\left|x+\dfrac{5}{2}\right|\le0\\ D_{max}=0\Leftrightarrow x=-\dfrac{5}{2}\)
Tính nhanh:
a) (-6,37 × 0,4) × 2,5;
b) (-0,125) × (-5,3) × 8;
c) (-2,5) × (-4) × (-7,9);
d) (-0,375) × 413(−2)3413(−2)3
Hướng dẫn làm bài:
a) (- 6,37 × 0,4) × 2,5
= - 6,37× (0,4 × 2,5)
= - 6,37 × 1 = - 6,37
b) (-0,125) × (-5,3) × 8
= (-0,125 × 8) × (-5,3)
=(-1). (-5,3) = 5,3
c) (-2,5) × (-4) × (-7,9)
= [(-2,5) × (-4)] × (-7,9)
= 10 . (-7,9)
= -79
d) (−0,375).413.(−2)3
=[(−0,375).(−8)].133=[(−0,375).(−8)].133
=3.133=13
a)\({\left( { - 2} \right)^2}.{\left( { - 2} \right)^3} = {\left( { - 2} \right)^{2 + 3}} = {\left( { - 2} \right)^5}\);
b)\({\left( { - 0,25} \right)^7}:{\left( { - 0,25} \right)^5} = {\left( { - 0,25} \right)^{7 - 5}} = {\left( { - 0,25} \right)^2} = {\left( {0,25} \right)^2}\);
c)\({\left( {\frac{3}{4}} \right)^4}.{\left( {\frac{3}{4}} \right)^3} = {\left( {\frac{3}{4}} \right)^{4 + 3}} = {\left( {\frac{3}{4}} \right)^7}.\)
\(A=\left(3\dfrac{1}{3}+2,5\right):\left(3\dfrac{1}{6}-4\dfrac{1}{5}\right)-\dfrac{11}{31}\\ =\left(\dfrac{10}{3}+\dfrac{5}{2}\right):\left(\dfrac{19}{6}-\dfrac{21}{5}\right)-\dfrac{31}{11}\\ =\left(\dfrac{30}{6}+\dfrac{15}{6}\right):\left(\dfrac{95}{30}-\dfrac{126}{30}\right)-\dfrac{31}{11}\\ =\dfrac{45}{6}:\dfrac{-21}{30}-\dfrac{31}{11}\\ =\dfrac{15}{2}\times\dfrac{-10}{7}-\dfrac{31}{11}=-\dfrac{75}{7}-\dfrac{31}{11}=-\dfrac{825}{77}-\dfrac{217}{77}=\dfrac{-1042}{77}\)
\(B=\left(-6\right).10:\left[-0,25+\dfrac{1}{2}:\left(-2\right)\right]+1\dfrac{3}{4}\\ =-60:\left(\dfrac{-1}{4}+\dfrac{1}{2}.\dfrac{-1}{2}\right)+1\dfrac{3}{4}\\ =-60:\left(\dfrac{-1}{4}+\dfrac{-1}{4}\right)+1\dfrac{3}{4}\\ =-60:\left(\dfrac{-1}{2}\right)+1\dfrac{3}{4}=120+1\dfrac{3}{4}=121\dfrac{3}{4}\)
\(\frac{72^2}{24^2}=\frac{3^2.24^2}{24^2}=3^2=9\)
\(\frac{\left(-7,5\right)^2}{2,5^2}=\frac{\left(7,5\right)^2}{\left(2,5\right)^2}=\frac{\left(2,5\right)^2.3^2}{\left(2,5\right)^2}=9\)
\(\frac{15^2}{27}=\frac{3^2.5^2}{27}=\frac{9.25}{27}=\frac{25}{3}\)
\(\frac{72^2}{24^2}=\left(\frac{72}{24}\right)^2=3^2=9\)
\(\frac{\left(-7,5\right)^3}{\left(2,5\right)^3}=\left(\frac{-7,5}{2,5}\right)^3=\left(-3\right)^3=-27\)
\(\frac{15^3}{27}=\frac{15^3}{3^3}=\left(\frac{15}{3}\right)^3=5^3=125\)
Chúc bạn hok tốt 
a)
\(7,5.\left(\frac{-2}{5}\right).\left(-2,5\right)\)
\(=7,5.\left[\left(\frac{-2}{5}\right).\left(-2,5\right)\right]\)
\(=7,5.1\)
\(=7,5\)
b)
\(\left(-50,5\right).8.\left(-0,25\right)\)
\(=\left(-50,5\right).\left[8.\left(-0,25\right)\right]\)
\(=\left(-50,5\right).\left(-2\right)\)
\(=101\)
c)
\(\left(0,125\right).\left(-3,7\right).\left(-2\right)^3\)
\(=\left(0,125\right).\left(-3,7\right).\left(-8\right)\)
\(=\left[\left(-8\right).\left(0,125\right)\right].\left(-3,7\right)\)
\(=\left(-1\right).\left(-3,7\right)\)
\(=3,7\)
Chúc cậu học tốt !!!