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a)( -11) .(8.9)= (-11) .8 - (-11) .9= 11
b) (-12).10 - (-9) . 10= [ -12 - (-9) ] . 10 = -30
a)\(\left(5^{2005}+5^{2004}+5^{2003}\right)\)
\(\Rightarrow5^{2003}.\left(5^2+5+1\right)\)
\(\Rightarrow5^{2003}.31⋮31\)
a. \(\left(-9\right).\left(-8\right)\) với \(0\)
\(\rightarrow72.....0\)
\(\rightarrow72>0\)
b. \(\left(-12\right).4\) với \(\left(-2\right).\left(-3\right)\)
\(\rightarrow\left(-48\right).......6\)
\(\rightarrow\left(-48\right)< 6\)
c. \(\left(+20\right).\left(+8\right)\) với \(\left(-19\right).\left(-9\right)\)
\(\rightarrow160......171\)
\(\rightarrow160< 171\)
d, \(\dfrac{-5}{9}+\dfrac{3}{5}-\dfrac{3}{9}+\dfrac{-2}{5}\)
\(=\left(\dfrac{-5}{9}+\dfrac{-3}{9}\right)+\left(\dfrac{3}{5}+\dfrac{-2}{5}\right)\)
\(=\dfrac{-8}{9}+\dfrac{1}{5}=-\dfrac{31}{45}\)
e) \(\left(\dfrac{1}{9}-\dfrac{9}{17}\right)+\dfrac{3}{6}-\left(\dfrac{12}{17}-\dfrac{1}{2}\right)+\dfrac{5}{9}\)
\(=\dfrac{1}{9}-\dfrac{9}{17}+\dfrac{3}{6}-\dfrac{12}{17}+\dfrac{1}{2}+\dfrac{5}{9}\)
\(=\left(\dfrac{1}{9}+\dfrac{5}{9}\right)+\left(\dfrac{-9}{17}+\dfrac{-12}{17}\right)+\left(\dfrac{1}{2}+\dfrac{1}{2}\right)\)
\(=\dfrac{2}{3}+\left(-1\right)+1\)
\(=\dfrac{2}{3}+0=\dfrac{2}{3}\)
\(7-\left\{12-\left[-\left(-3\right)+\left(-10\right)-\left(-11\right)\right]-\left[-\left(-9\right)+\left(-8\right)-12\right]\right\}\)\(-\left(-4\right)\)
= \(7-\left\{12-\left[3+\left(-10\right)+11\right]-\left[9+\left(-8\right)-12\right]\right\}\) \(+4\)
= \(7-\left\{12-\left[7+11\right]-\left[1-12\right]\right\}+4\)
= \(7-\left\{12-18-\left(-11\right)\right\}+4\)
= \(7-\left\{-6+11\right\}+4\)
= \(7-5+4\)
= 6
7 - { 12 - [ - (- 3) + (- 10) - (- 11) ] - [ - (- 9) + (- 8) - (+ 12) ] } - (- 4)
= 7 - [ 12 - ( 3 - 10 + 11 ) - ( 9 - 8 - 12 ) ] + 4
= 7 - ( 12 - 4 + 11 ) + 4
=7 - 19 + 4
= - 8
a)\(\frac{11^4.6-11^5}{11^4-11^5}:\frac{9^8.3-9^9}{9^8.5+9^8.7}\)
\(=1.6:\frac{9^8.3-9^8.9}{9^8.\left(5+7\right)}\)
\(=6:\frac{9^8.\left(3-9\right)}{9^8.12}\)
\(=6:\frac{9^8.\left(-6\right)}{9^8.12}\)
\(=6:\left(-\frac{6}{12}\right)\)
\(=6:\left(-\frac{1}{2}\right)\)
\(=-12\)
b) 3/5 : ( -1/5-1/6)+3/5:(-1/3-16/15) ( mình chuyển về ps luôn )
=3/5: (-11/30) + 3/5 : (-7/5)
=3/5:[-11/30+(-7/5)]
=3/5:53/30
=18/53
c) (1/2-13/14):5/7-(-2/21+1/7):5/7
= -3/7:5/7-1/21:5/7
=(-3/7-1/21):5/7
=-10/21:5/7
=-2/3
câu b vá c mình làm tắt nha. chúc bạn học tốt
\(\left(\dfrac{2}{3}\right)^3.\left(\dfrac{-3}{4}\right)^2.\left(-1\right)^{2013}=\dfrac{8}{27}.\dfrac{9}{16}.\left(-1\right)=-\dfrac{1}{6}\)
\(\left(\dfrac{1}{5}\right)^{15}.\left(\dfrac{1}{4}\right)^{20}=\dfrac{1}{5^{12}}.\dfrac{1}{4^{20}}=5^{-12}.4^{-20}=125^{-4}.1024^{-4}=\left(125.1024\right)^{-4}=128000^{-4}\)
\(\dfrac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}=\dfrac{2^{12}.3^{10}+2^3.3.5.2^9.3^9}{2^{12}.3^{12}+2^{11}.3^{11}}=\dfrac{2^{12}.3^{10}+2^{12}.2^{10}.5}{2^{12}.3^{12}+2^{11}.3^{11}}=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}\left(2.3+1\right)}=\dfrac{2.6}{3.7}=\dfrac{4}{7}\)
\([\left(-9\right).\left(-9\right).\left(-9\right)+9^3]:8^{10}\)
\(=[\left(-729\right)+729]:8^{10}\)
\(=0\)
= ( -729 + 729) : 8^10
= 0: 8^10
= 0