Đáp án:

Giải thích các bước giải:

 Câu 11: 

a)7×3²-24:2³=7.9-24:8=63-3=60

b) 28.78+28.13+28.9=28.(78+13+9)=78.100=7800

c) 4.{3²[(5²+2³):11]-26}+2002=3.{9[(25+8):11]-26}+2002=3[9(33:11)-26]+2002=3(27-26)+2002

=3+2002=2005

d) 11400:{[(15.3-21):4]+108}=11400:[(24:4)+108]=11400:(6+108)=11400:114=100

Câu 12

a) 70-5(x-3)=45

⇒70-5x+15=45

⇒70+15-45=5x

40=5x

x=8

b) (x-10)6=18

6x-60=18

6x=60+18=78

x=78:6=13

c)5^x.5³=125

5^x=125:125=1

5^x=5^0

x=0

Câu 13

a) Số số hạng là: (159-1):2+1=80 số

Số cặp là 80:2=40

⇒A= (1+159)40=6400

b) B=3+3²+3³+....+3^2010

⇒2B=3²+3³+..+3^2011

2B-B=3+3^2011

c) A=2+2²+2³+.....+2^2010=(2+2²)+(2³+2^4)+....+.(2^2009+2^2010)=

2(1+2)+2³(1+2)+...+2^2009(1+2)=3.2+3.2³+...+3.2^2009=3(2+2³+....+2^2009)

Vì 3 chia hết cho 3⇒3(2+2³+....+2^2009) chia hết cho 3⇒A chia hết cho 3

A=2+2²+2³+.....+2^2010=(2+2²+2³)+.....(2^2008+2^2009+2^2010)=

2(1+2+4)+...+2^2008(1+2+4)=7.2+...+7.2^2008=7(2++....+2^2008)

Vì 7 chia hết cho 7⇒7(2+....+2^2008) chia hết cho 7⇒A chia hết cho 7

Đáp án:

$\displaystyle \begin{array}{{>{\displaystyle}l}} Câu\ 10:\ D\\ Câu\ 11:\\ a.\ 60;\ b.\ 2800;\ c.\ 2006;\ d.\ 100\\ Câu\ 12:\\ a.\ x=8;\ b.\ x=13;\ c.\ x=0\\ Câu\ 13:\\ a.\ A=6400;\ b.\ B=\frac{3^{2011} -3}{2} \end{array}$

Giải thích các bước giải:

$\displaystyle \begin{array}{{>{\displaystyle}l}} Câu\ 10:\\ 2^{x} =16=2^{4} \Leftrightarrow x=4\Leftrightarrow D\ đúng\\ TỰ\ LUẬN:\\ Câu\ 11:\\ a.\ 7.3^{2} -24:2^{3} =7.3^{2} -3=3( 7.3-1) =3.20=60\\ b.\ 28.78+28.13+28.9=28.( 78+13+9) =28.100=2800\\ c.\ 4.\left\{3^{2} .\left[\left( 5^{2} +2^{3}\right) :11\right] -26\right\} +2002\\ =4.\left[ 3^{2} .( 33:11) -26\right] +2002\\ =4.( 27-26) +2002=4+2002=2006\\ d.\ 11400:\ \{[( 5.3-21) :4] +108\}\\ =11400:\{[ 3.( 15-7)] :4+3.36\}\\ =11400:[( 3.8) :4+3.36] =11400:[ 3.( 2+36)]\\ =11400:114=100\\ Câu\ 12:\\ a.\ 70-5( x-3) =45\\ \Leftrightarrow 5( x-3) =25\Leftrightarrow x-3=5\Leftrightarrow x=8\\ b.\ ( x-10) .6=18\Leftrightarrow x-10=3\Leftrightarrow x=13\\ d.\ 5^{x} .5^{3} =125=5^{3} \Leftrightarrow 5^{x} =1=5^{0} \Leftrightarrow x=0\\ Câu\ 13:\\ a.\ A=1+3+5+7+9+...+157+159\\ =( 1+159) +( 3+157) +....+( 77+83) +( 79+81)\\ =160.40=6400\\ b.\ B=3^{1} +3^{2} +3^{3} +...+3^{2010}\\ \Leftrightarrow 3B=3^{2} +3^{3} +3^{4} +...+3^{2011}\\ \Leftrightarrow 3B-B=\left( 3^{2} +3^{3} +...+3^{2011}\right) -\left( 3^{1} +3^{2} +...+3^{2010}\right)\\ \Leftrightarrow 2B=3^{2011} -3\Leftrightarrow B=\frac{3^{2011} -3}{2}\\ c.\ A=2^{1} +2^{2} +2^{3} +...+2^{2010}\\ =2( 1+2) +2^{3}( 1+2) +......+2^{2009}( 1+2)\\ =3.\left( 2+2^{3} +....+2^{2009}\right) \Leftrightarrow A\vdots 3\ ( 1)\\ Lại\ có:\ A=2^{1} +2^{2} +2^{3} +...+2^{2010}\\ =2\left( 1+2+2^{2}\right) +2^{4}\left( 1+2+2^{2}\right) +...+2^{2008}\left( 1+2+2^{2}\right)\\ =7.\left( 2+2^{4} +...+2^{2008}\right) \Leftrightarrow A\vdots 7\ ( 2)\\ Từ\ ( 1) \ và\ ( 2) \Rightarrow đpcm \end{array}$