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\(\frac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}=\frac{2^{10}.3^9\left(3-1\right)}{2^9.3^{10}}=\frac{2.2}{3}=\frac{4}{3}\)
câu sau tương tự nhé
\(\dfrac{16^3.3^{10}+144.6^9}{4^6.3^{12}+6^{11}}\)
=\(\dfrac{16^3.3^{10}+144.6^9}{4.4.4.4.4.4.3^{12}+6^{11}}\)
=\(\dfrac{16^3.3^{10}+144.6^9}{16.16.16.3^{12}+6^{11}}\)
=\(\dfrac{16^3.3^{10}+4.6^2.6^9}{16^3.3^{12}+6^{11}}\)
=\(\dfrac{4.6^{11}}{3^2+6^{11}}\)
=\(\dfrac{4}{9}\)
Ko chắc
tử số 46.310+144.69 = 212.310+2.23.3.3.69
= 69.(23.3)+(23.3).69.6 = 69.(23.3).(6+1) = 69.(23.3).7 = 69.2.3.22.7
= 610.4.7
mẫu số 46.312+611 = 212.312+611 = 612+611 = 611.6+611
= 611.(6+1) = 611.7
\(\dfrac{16^{3}.3^{10}+144.6^{9}}{4^{6}.3^{12}.6^{11}}=\dfrac{6^{10}.4.7}{6^{11}.7}\)=\(\dfrac{4}{6}=\dfrac{2}{3}\)
mà cậu trình bày trên phân số nhé để nhanh thì mình chia ra thôi
2:
\(B=3^{n+2}-2^{n+2}+3^n-2^n\)
\(=3^n\cdot9+3^n-2^n\cdot4-2^n\)
\(=3^n\cdot10-2^n\cdot5\)
\(=3^n\cdot10-2^{n-1}\cdot10⋮10\)
`a)1/2 . [-3]/4 . [-5]/8 . [-8]/9=[1. (-3).(-5).(-8)]/[2.4.8.3.3]=[-5]/[2.4.3]=[-5]/24`
`b)(2/[1.3]+2/[3.5]+2/[5.7]).([10.13]/3-[2^2]/3-[5^3]/3)`
`=(1-1/3+1/3-1/5+1/5-1/7).[10.13-2^2-5^3]/3`
`=(1-1/7).[130-4-125]/3`
`=6/7 . 1/3 = 2/7`
____________________________________________________
`8/9+1/9 . 2/9+1/9 . 7/9`
`=8/9+1/9.(2/9+7/9)`
`=8/9+1/9 . 9/9`
`=8/9+1/9=9/9=1`
a) \(\dfrac{1}{2}\cdot\dfrac{-3}{4}\cdot\dfrac{-5}{8}\cdot\dfrac{-8}{9}\)
\(=\dfrac{1\cdot\left(-3\right)\cdot\left(-5\right)\cdot\left(-8\right)}{2\cdot4\cdot8\cdot9}\)
\(=-\dfrac{5}{24}\)
b) \(\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}\right)\cdot\left(\dfrac{10\cdot13}{3}-\dfrac{2^2}{3}-\dfrac{5^3}{3}\right)\)
\(=\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}\right)\cdot\left(\dfrac{130}{3}-\dfrac{4}{3}-\dfrac{125}{3}\right)\)
\(=\left(1-\dfrac{1}{7}\right)\cdot\dfrac{1}{3}\)
\(=\dfrac{6}{7}\cdot\dfrac{1}{3}\)
\(=\dfrac{2}{7}\)
\(\dfrac{8}{9}+\dfrac{1}{9}\cdot\dfrac{2}{9}+\dfrac{1}{9}\cdot\dfrac{7}{9}\)
\(=\dfrac{8}{9}+\dfrac{2}{81}+\dfrac{7}{81}\)
\(=\dfrac{72}{81}+\dfrac{2}{81}+\dfrac{7}{81}\)
\(=1\)
3/ \(2\left(x-3\right)-3\left(1-2x\right)=4+4\left(1-x\right)\)
\(\Leftrightarrow2x-6-3+6x=4+4-4x\)
\(\Leftrightarrow8x-9=8-4x\)
\(\Leftrightarrow8x+4x=8+9\)
\(\Leftrightarrow12x=17\)
\(\Leftrightarrow x=\dfrac{17}{12}\)
Vậy \(x=\dfrac{17}{12}\)
4/ \(\dfrac{x-2}{2}-\dfrac{1+x}{3}=\dfrac{4-3x}{4}-1\)
\(\Leftrightarrow6\left(x-2\right)-4\left(1+x\right)=3\left(4-3x\right)-12\)
\(\Leftrightarrow6x-12-4-4x=12-9x-12\)
\(\Leftrightarrow6x-4-4x=12-9x\)
\(\Leftrightarrow2x-4=12-9x\)
\(\Leftrightarrow2x+9x=12+4\)
\(\Leftrightarrow11x=16\)
\(\Leftrightarrow x=\dfrac{16}{11}\)
Vậy \(x=\dfrac{16}{11}\)
a)\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)
\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(=\frac{1}{2}.\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+\frac{11-9}{9.11}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{11}\right)\)
\(\frac{10}{22}\)
\(\dfrac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
\(=\dfrac{11.3^{29}-\left(3^2\right)^{15}}{2^2.3^{28}}\)
\(=\dfrac{11.3^{29}-3^{30}}{2^2.3^{28}}\)
\(=\dfrac{3^{29}\left(11-3\right)}{2^2.3^{28}}\)
\(=\dfrac{3^{29}.2^3}{2^2.3^{28}}\)
\(=\dfrac{3.2}{1.1}=6\)
\(\dfrac{11.3^{22}.3^7-9^{15}}{2^2.3^{28}}\)
\(=\dfrac{11.3^{28}.3-9^{15}}{2^2.3^{28}}\)
\(=\dfrac{11.3-9^{15}}{2^2}\)
\(=\dfrac{33-9^{15}}{4}\)
\(\dfrac{11.3^{22}.3^7-9^{15}}{2^2.3^{28}}\)
=\(\dfrac{11.3^{29}-\left(3^2\right)^{15}}{2^2.3^{28}}\)
=\(\dfrac{11.3^{29}-3^{30}}{2^2.3^{28}}\)
=\(\dfrac{3^{29}.\left(11-3\right)}{2^2.3^{28}}\)
=\(\dfrac{3^{29}.8}{2^2.3^{28}}\)
=\(\dfrac{3^{29}.2^3}{2^2.3^{28}}\)
=3.2
=6
Đè là sao đây bạn!!Mik không hiểu đề cho lắm...........
Bạn viết lại đề cho mik nha!!!