\(\left(\dfrac{1}{10}\right)^{15}\)và \(\left(\dfrac{3...">
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17 tháng 9 2021

Ta có:

\(\left(\dfrac{1}{10}\right)^{15}=\left(\left(\dfrac{1}{10}\right)^3\right)^5=\left(\dfrac{1}{1000}\right)^5\)

\(\left(\dfrac{3}{10}\right)^{20}=\left(\left(\dfrac{3}{10}\right)^4\right)^5=\left(\dfrac{81}{10000}\right)^5\)

17 tháng 9 2021

Ta có: \(\left(\dfrac{1}{10}\right)^{15}=\left(\dfrac{1}{10}^3\right)^5=\left(\dfrac{1}{1000}\right)^5\)

\(\left(\dfrac{3}{10}\right)^{20}=\left(\dfrac{3}{10}^4\right)^5=\left(\dfrac{3}{10000}\right)^5\)

Vì \(\dfrac{1}{1000}>\dfrac{3}{10000}\) nên \(\left(\dfrac{1}{10}\right)^{15}>\left(\dfrac{3}{10}\right)^{20}\)

a: \(=0.5\cdot10-\dfrac{1}{7}+15=20-\dfrac{1}{7}=\dfrac{139}{7}\)

b: \(=6\cdot\dfrac{-2}{3}+12\cdot\dfrac{4}{9}+18\cdot\dfrac{-8}{27}\)

\(=-4+\dfrac{16}{3}-\dfrac{16}{3}=-4\)

c: \(=\left(\dfrac{5}{2}+\dfrac{3}{8}-\dfrac{5}{8}+\dfrac{2}{3}\right):\left(\dfrac{17}{2}+\dfrac{49}{4}-\dfrac{17}{8}+\dfrac{34}{15}\right)\)

\(=\dfrac{35}{12}:\dfrac{2507}{120}=\dfrac{350}{2507}\)

4 tháng 7 2018

\(\left(\dfrac{1}{16}\right)^{10}=\left[\left(\dfrac{1}{2}\right)^4\right]^{10}=\left(\dfrac{1}{2}\right)^{40}< \left(\dfrac{1}{2}\right)^{50}\\ \left(\dfrac{1}{2}\right)^{300}=\left(\dfrac{1}{2}\right)^{3\cdot100}=\left[\left(\dfrac{1}{2}\right)^3\right]^{100}=\left(\dfrac{1}{8}\right)^{100}\\ \left(\dfrac{1}{3}\right)^{200}=\left(\dfrac{1}{3}\right)^{2\cdot100}=\left[\left(\dfrac{1}{3}\right)^2\right]^{100}=\left(\dfrac{1}{9}\right)^{100}\\ \dfrac{1}{8}>\dfrac{1}{9}\Rightarrow\left(\dfrac{1}{8}\right)^{100}>\left(\dfrac{1}{9}\right)^{100}\Rightarrow\left(\dfrac{1}{2}\right)^{300}>\left(\dfrac{1}{3}\right)^{200}\\ \left(0,3\right)^{20}=\left(0,3\right)^{2\cdot10}=\left[\left(0,3\right)^2\right]^{10}=\left(0,09\right)^{10}< \left(0,1\right)^{10}\)

5 tháng 7 2018

a) \(\left[\left(\dfrac{1}{2}\right)^4\right]^{10}=\left(\dfrac{1}{2}\right)^{40}\)

\(\Rightarrow\left(\dfrac{1}{2}\right)^{40}< \left(\dfrac{1}{2}\right)^{50}\)

\(40< 50\)

b)\(\left[\left(\dfrac{1}{2}\right)^3\right]^{100}=\left(\dfrac{1}{8}\right)^{100}\)

\(\left[\left(\dfrac{1}{3}\right)^2\right]^{100}=\left(\dfrac{1}{9}\right)^{100}\)

\(\Rightarrow\text{​​}\text{​​}\left(\dfrac{1}{2}\right)^{300}>\left(\dfrac{1}{3}\right)^{200}\)

\(\dfrac{1}{8}>\dfrac{1}{9}\)

c)\(\left[\left(0,3\right)^2\right]^{10}=\left(0,09\right)^{10}\)

\(\Rightarrow\left(0,1\right)^{10}>\left(0,3\right)^{20}\)

\(0,1>0,09\)

8 tháng 10 2017

*** \(\dfrac{15-x}{8}=\dfrac{x-23}{10}\)

\(\Rightarrow10\left(15-x\right)=8\left(x-23\right)\)

\(\Rightarrow150-10x=8x-184\)

\(\Rightarrow150+184=10x+8x\)

\(\Rightarrow18x=334\)

\(\Rightarrow x=\dfrac{167}{9}\)

*** \(\dfrac{1}{2}\left|2x-1\right|-3\dfrac{2}{5}=\left(-\dfrac{1}{2}\right).\left(2015\right)^0\)

\(\Rightarrow\dfrac{1}{2}\left|2x-1\right|-3\dfrac{2}{5}=\left(-\dfrac{1}{2}\right).1\)

\(\Rightarrow\dfrac{1}{2}\left|2x-1\right|-3\dfrac{2}{5}=\left(-\dfrac{1}{2}\right)\)

\(\Rightarrow\dfrac{1}{2}\left|2x-1\right|-3\dfrac{2}{5}=\left(-\dfrac{1}{2}\right)\)

\(\Rightarrow\dfrac{1}{2}\left|2x-1\right|=\left(-\dfrac{1}{2}\right)+3\dfrac{2}{5}\)

\(\Rightarrow\dfrac{1}{2}\left|2x-1\right|=\dfrac{29}{10}\)

\(\Rightarrow\left|2x-1\right|=\dfrac{29}{10}:\dfrac{1}{2}\)

\(\Rightarrow\left|2x-1\right|=\dfrac{29}{5}\)

\(\Rightarrow\left[{}\begin{matrix}2x-1=\dfrac{29}{5}\\2x-1=-\dfrac{29}{5}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=\dfrac{34}{5}\\2x=-\dfrac{24}{5}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{17}{5}\\x=-\dfrac{12}{5}\end{matrix}\right.\)

AH
Akai Haruma
Giáo viên
8 tháng 10 2017

Bài 2 từ dòng 2 đến dòng 7 nên dùng dấu \(\Leftrightarrow \) mới đúng em nhé.

a: TH1: x>=0

=>x+x=1/3

=>x=1/6(nhận)

TH2: x<0

Pt sẽ là -x+x=1/3

=>0=1/3(loại)

b: \(\Leftrightarrow\left\{{}\begin{matrix}x>=0\\x^2-x-2=0\end{matrix}\right.\Leftrightarrow x=2\)

c: \(\Leftrightarrow\dfrac{1}{x-1}-\dfrac{1}{x-3}+\dfrac{1}{x-3}-\dfrac{1}{x-8}+\dfrac{1}{x-8}-\dfrac{1}{x-20}-\dfrac{1}{x-20}=\dfrac{-3}{4}\)

\(\Leftrightarrow\dfrac{1}{x-1}-\dfrac{2}{x-20}=\dfrac{-3}{4}\)

\(\Leftrightarrow\dfrac{x-20-2x+2}{\left(x-1\right)\left(x-20\right)}=\dfrac{-3}{4}\)

\(\Leftrightarrow-3\left(x^2-21x+20\right)=4\left(-x-18\right)\)

\(\Leftrightarrow3x^2-63x+60=4x+72\)

=>3x^2-67x-12=0

hay \(x\in\left\{22.51;-0.18\right\}\)

24 tháng 7 2017

|2x-1|=1,5

TH(1)2x-1=1,5

2x =1,5+1

2x =2,5

x =2,5 :2

x =1,25

TH(2) 2x-1=-1,5

2x =-1,5+1

2x =-0,5

x =-0,5:2

x =-0,25

các câu khác cứ tương tự bạn nhé

24 tháng 7 2017

b) \(7,5-\left|5-2x\right|=-4,5\)

\(\left|5-2x\right|=7,5+4,7\)

\(\left|5-2x\right|=12\)

th1 :\(5-2x=12\)

\(2x=5-12\)

\(2x=-7\)

\(x=-7:2\)

\(x=-3,5\)

th2: \(5-2x=-12\)

\(2x=5+12\)

\(2x=17\)

\(x=17:2\)

\(x=8,5\)

c) \(-3+\left|x\right|=-1\)

\(\left|x\right|=-1+3\)

\(\left|x\right|=2\)

th1: \(x=-2\)

th2 : \(x=2\)

d)\(\left|2\dfrac{1}{3}-x\right|=\dfrac{1}{6}\)

\(\left|\dfrac{7}{3}-x\right|=\dfrac{1}{6}\)

th1 :\(\dfrac{7}{3}-x=\dfrac{1}{6}\)

\(x=\dfrac{7}{3}-\dfrac{1}{2}\)

\(x=\dfrac{11}{6}\)

th2: \(\dfrac{7}{3}-x=\dfrac{-1}{6}\)

\(x=\dfrac{7}{3}+\dfrac{1}{6}\)

\(x=\dfrac{-5}{2}\)

e) \(\dfrac{5}{7}-\left|x+1\right|=\dfrac{1}{14}\)

\(\left|x+1\right|=\dfrac{5}{7}-\dfrac{1}{14}\)

\(\left|x+1\right|=\dfrac{9}{14}\)

th1 :\(x+1=\dfrac{9}{14}\)

\(x=\dfrac{9}{14}-1\)

\(x=\dfrac{-5}{14}\)

th2 : \(x+1=\dfrac{-9}{14}\)

\(x=\dfrac{-9}{14}-1\)

\(x=\dfrac{-5}{14}\)

24 tháng 7 2017

\(\dfrac{2^{19}+27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)

\(=\dfrac{2^{19}+\left(3^3\right)^3+5.3.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(3.4\right)^{10}}\)

\(=\dfrac{2^{19}.3^9+3.5.2^{18}.3^8}{3^9.2^9.2^{10}+3^{10}.4^{10}}\)

\(=\dfrac{2^{19}.3^9+5.2^{18}.3^9}{3^9.2^{19}+3^{10}.\left(2^2\right)^{10}}\)

\(=\dfrac{2^{18}.3^9.\left(2.5\right)}{3^9.2^{19}+3^{10}.2^{20}}\)

\(=\dfrac{2^{18}.3^9.7}{2^{19}.3^9.\left(1+3.2\right)}\)

\(=\dfrac{7}{2\left(1+6\right)}\)

\(=\dfrac{7}{2.7}\)

\(=\dfrac{1}{2}\)

a) \(5^{20}và2550^{10}\)

\(5^{20}=\left(5^2\right)^{10}=25^{10}< 2550^{10}\)

=> \(5^{20}< 2550^{10}\)

b) \(999^{10}và999999^5\)

\(999^{10}=\left(999^2\right)^5=1998^5< 999999^5\)

=> \(999^{10}< 999999^5\)

c) \(\left(\dfrac{-1^{300}}{5}\right)và\left(\dfrac{-1^{500}}{3}\right)\)

\(\left(\dfrac{-1^{300}}{5}\right)=\dfrac{-1}{5}\)

\(\left(\dfrac{-1^{500}}{3}\right)=\dfrac{-1}{3}\)

\(\dfrac{-1}{5}=\dfrac{-3}{15}\)

\(\dfrac{-1}{3}=\dfrac{-5}{15}\)

=> \(\dfrac{-3}{15}>\dfrac{-5}{15}\)

=> \(\left(\dfrac{-1^{300}}{5}\right)>\left(\dfrac{-1^{500}}{3}\right)\)

20 tháng 8 2017

thank you very much

16 tháng 9 2017

cái này mà bạn ko biết làm á, bấm máy tính tạch tạch mấy phát là ra mà

17 tháng 9 2017

lười làm nên nhờ mấy bạn giải dùm

14 tháng 7 2017

cứ phan tích cho hết đi là đc 9^6. 9^10 = (3^2)^6...................

tự làm đi

14 tháng 7 2017

1. Tính:

a. \(\dfrac{9^6.9^{10}}{3^{32}}=\dfrac{\left(3^2\right)^6.\left(3^2\right)^{10}}{3^{32}}=\dfrac{3^{12}.3^{20}}{3^{32}}=\dfrac{3^{32}}{3^{32}}=1\)

b. \(\dfrac{25^8.25^{10}}{5^{34}}=\dfrac{\left(5^2\right)^8.\left(5^2\right)^{10}}{5^{34}}=\dfrac{5^{16}.5^{20}}{5^{34}}=\dfrac{5^{36}}{5^{34}}=5^{36}:5^{34}=5^2=25\)

c. \(\dfrac{7^{56}}{49^9.49^{20}}=\dfrac{7^{56}}{\left(7^2\right)^9.\left(7^2\right)^{20}}=\dfrac{7^{56}}{7^{18}.7^{40}}=\dfrac{7^{56}}{7^{58}}=7^{56}:7^{58}=\dfrac{7^{56}}{7^{56}.7^2}=\dfrac{1}{7^2}=\dfrac{1}{49}\)

d. \(\dfrac{4^2.4^3}{2^{10}}=\dfrac{\left(2^2\right)^2.\left(2^2\right)^3}{2^{10}}=\dfrac{2^4.3^6}{2^{10}}=\dfrac{2^{10}}{2^{10}}=1\)

e. \(\dfrac{2^{17}.25^5}{10^8.8^3}=\dfrac{2^{17}.\left(5^2\right)^5}{\left(2.5\right)^8.\left(2^3\right)^3}=\dfrac{2^{17}.5^{10}}{2^8.5^8.2^9}=\dfrac{2^{17}.5^{10}}{2^{17}.5^8}=\dfrac{5^{10}}{5^8}=5^{10}:5^8=5^2=25\)

f. \(\dfrac{3^{15}.25^4}{15^6.27^3}=\dfrac{3^{15}.\left(5^2\right)^4}{\left(3.5\right)^6.\left(3^3\right)^3}=\dfrac{3^{15}.5^8}{5^6.3^6.3^9}=\dfrac{3^{15}.5^8}{5^6.3^6.3^9}=\dfrac{5^8}{5^6}=5^8:5^6=5^2=25\)

2. Tính lũy thừa âm:

a. 3-2 = \(\dfrac{1}{3^2}\) = \(\dfrac{1}{9}\)

b. 2-3 = \(\dfrac{1}{2^3}\) = \(\dfrac{1}{8}\)

3. Tính :

a. \(\dfrac{\left(0,8\right)^4}{\left(0,4\right)^3}=\dfrac{\left(0,8\right)^3.0,8}{\left(0,4\right)^3}=\left(\dfrac{0,8}{0,4}\right)^3.0,8=2^3.0,8=8.0,8=6,4\)

b. \(\dfrac{\left(0,8\right)^3}{\left(0,4\right)^4}=\dfrac{\left(0,8\right)^3}{\left(0,4\right)^3:0,4}=\left(\dfrac{0,8}{0,4}\right)^3.\dfrac{1}{0,4}=2^3.2,5=8.2,5=20\)

c. \(\dfrac{\left(0,6\right)^5}{\left(0,2\right)^6}=\dfrac{\left(0,6\right)^5}{\left(0,2\right)^5.\left(0,2\right)}=\left(\dfrac{\left(0,6\right)}{\left(0,2\right)}\right)^5.\dfrac{1}{0,2}=3^5.\dfrac{1}{0,2}=\dfrac{3^5}{0,2}=1215\)

P/s : Chế Mai Ngọc Trâm thử tham khảo thử đi!!!

b: \(\left(\dfrac{2}{5}-\dfrac{7}{10}x\right):\dfrac{5}{3}=-\dfrac{3}{4}\)

\(\Leftrightarrow\dfrac{2}{5}-\dfrac{7}{10}x=\dfrac{-3}{4}\cdot\dfrac{5}{3}=\dfrac{-5}{4}\)

\(\Leftrightarrow x\cdot\dfrac{7}{10}=\dfrac{2}{5}+\dfrac{5}{4}=\dfrac{8+25}{20}=\dfrac{33}{20}\)

\(\Leftrightarrow x=\dfrac{33}{20}:\dfrac{7}{10}=\dfrac{33}{20}\cdot\dfrac{10}{7}=\dfrac{33}{14}\)

c: \(\dfrac{7}{16}:\left(\dfrac{1}{4}x+\dfrac{9}{2}\right)-\dfrac{11}{6}=0\)

\(\Leftrightarrow\dfrac{7}{16}:\left(\dfrac{1}{4}x+\dfrac{9}{2}\right)=\dfrac{11}{6}\)

\(\Leftrightarrow x\cdot\dfrac{1}{4}+\dfrac{9}{2}=\dfrac{11}{6}:\dfrac{7}{16}=\dfrac{88}{21}\)

\(\Leftrightarrow x\cdot\dfrac{1}{4}=\dfrac{88}{21}-\dfrac{9}{2}=-\dfrac{13}{42}\)

hay \(x=-\dfrac{26}{21}\)