Chứng minh : \(\frac{\left(5^4-5^3\right)}{125^4}=\frac{64}{125}\)
Tìm x
a)\(^{3^x}+^{3^{x+2}}=810\)
b)\(\left(x+\frac{2017}{2018}\right)^6=0\)
Tìm x, biết:
a) \(\left(\frac{-3}{4}\right)^{3x-1}=\frac{-27}{64}\)
b) \(\left(\frac{4}{5}\right)^{2x+5}=\frac{256}{265}\)
c) \(\frac{\left(x+3\right)^5}{\left(x+3\right)^2}=\frac{64}{27}\)
d) \(\left(x-\frac{2}{15}\right)^3=\frac{8}{125}\)
a) \(\left(-\frac{3}{4}\right)^{3x-1}=\frac{-27}{64}\)
\(\Leftrightarrow\left(-\frac{3}{4}\right)^{3x-1}=\left(-\frac{3}{4}\right)^3\)
\(\Leftrightarrow3x-1=3\)
\(\Leftrightarrow3x=4\)
\(\Leftrightarrow x=\frac{4}{3}\)
b) Đề sai ! Sửa :
\(\left(\frac{4}{5}\right)^{2x+5}=\frac{256}{625}\)
\(\Leftrightarrow\left(\frac{4}{5}\right)^{2x+5}=\left(\frac{4}{5}\right)^4\)
\(\Leftrightarrow2x+5=4\)
\(\Leftrightarrow2x=-1\)
\(\Leftrightarrow x=-\frac{1}{2}\)
c) \(\frac{\left(x+3\right)^5}{\left(x+5\right)^2}=\frac{64}{27}\)
\(\Leftrightarrow\left(x+3\right)^3=\left(\frac{4}{3}\right)^3\)
\(\Leftrightarrow x+3=\frac{4}{3}\)
\(\Leftrightarrow x=-\frac{5}{3}\)
d) \(\left(x-\frac{2}{15}\right)^3=\frac{8}{125}\)
\(\Leftrightarrow\left(x-\frac{2}{15}\right)^3=\left(\frac{2}{15}\right)^3\)
\(\Leftrightarrow x-\frac{2}{15}=\frac{2}{15}\)
\(\Leftrightarrow x=\frac{4}{15}\)
Bài 1: Thực hiện phép tính:
a, \(3\frac{1}{2}-\frac{1}{2}.\left(-4,25-\frac{3}{4}\right)^2:\frac{5}{4}\)
b, \(\frac{3}{7}.1\frac{1}{2}+\frac{3}{7}.0,5-\frac{3}{7}.9\)
c, \(\frac{125^{2016}.8^{2017}}{50^{2017}.20^{2018}}\)
d, \(\frac{4^{2002}.9^{1001}}{16^{1001}.3^{2003}}\)
e, \(\sqrt{25-16}-\left|-3,7+0,7\right|\)
Bài 2: Tìm x
a, \(\frac{1}{3}x+\frac{4}{5}=3\frac{4}{5}\)
b, \(\left|x+\frac{3}{4}\right|-2,25=1\frac{3}{4}\)
c, \(\left(-x+\frac{2}{5}\right)^4=\frac{1}{16}\)
d, \(\left(\frac{2}{5}\right)^{3x}:\left(\frac{4}{3}\right)^{21}=\left(\frac{6}{20}\right)^{21}\)
e, \(\frac{-x}{\frac{3}{5}}=\frac{\frac{27}{5}}{-x}\)
g, \(x:1\frac{1}{2}=-2,5:2\frac{1}{5}\)
\(3\frac{1}{2}-\frac{1}{2}.\left(-4,25-\frac{3}{4}\right)^2:\frac{5}{4}\)
\(=\frac{7}{2}-\frac{1}{2}.\left(-4,25-0,75\right)^2:\frac{5}{4}\)
\(=\frac{7}{2}-\frac{1}{2}.\left(-5\right)^2:\frac{5}{4}\)
\(=\frac{7}{2}-\frac{1}{2}.5.\frac{4}{5}\)
\(=\frac{7}{2}-2\)
\(=\frac{7}{2}-\frac{4}{2}\)
\(=\frac{3}{2}\)
\(\frac{3}{7}.1\frac{1}{2}+\frac{3}{7}.0,5-\frac{3}{7}.9\)
\(=\frac{3}{7}.\left(\frac{3}{2}+\frac{1}{2}-9\right)\)
\(=\frac{3}{7}.\left(2-9\right)\)
\(=\frac{3}{7}.\left(-7\right)\)
\(=-3\)
\(\frac{125^{2016}.8^{2017}}{50^{2017}.20^{2018}}=\frac{\left(5^3\right)^{2016}.\left(2^3\right)^{2017}}{\left(5^2\right)^{2017}.2^{2017}.\left(2^2\right)^{2018}.5^{2018}}=\frac{\left(5^3\right)^{2016}.\left(2^3\right)^{2017}}{\left(5^3\right)^{2017}.\left(2^3\right)^{2017}.2.5}=\frac{1}{5^4.2}=\frac{1}{1250}\)( tính nhẩm, ko chắc đúng )
1
a) \(3\frac{1}{2}-\frac{1}{2}\cdot\left(-4,25-\frac{3}{4}\right)^2\) : \(\frac{5}{4}\)
= \(3\cdot25:\frac{5}{4}\)
= \(3\cdot\left(25:\frac{5}{4}\right)\)
=\(3\cdot20\)
=60
b)=\(\frac{3}{7}\cdot\left(1\frac{1}{2}+0,5-9\right)\)
=\(\frac{3}{7}\cdot\left(-7\right)\)
=\(-3\)
c) =
Chứng minh : \(\frac{\left(5^4-5^3\right)^3}{125^4}=\frac{64}{125}\)
Tim x biet
k) \(\left[\left(3,75:\frac{1}{4}+2\frac{2}{5}.125\%\right)-\left(\frac{7}{2}.0,8-1,2:\frac{3}{2}\right)\right]:\left(1\frac{1}{2}+0,75\right)x=64\)
Bài 1: Tính
a, \(22\frac{1}{2}.\frac{7}{9}+50\%-1,25\)
b,1,4\(.\frac{15}{49}-\left(\frac{4}{5}+\frac{2}{3}\right):2\frac{1}{5}\)
c,\(125\%.\left(-\frac{1}{2}\right)^2:\left(1\frac{5}{6}-1,6\right)+2016^0\)
d,1,4 .\(\frac{15}{49}-\left(20\%+\frac{2}{3}\right):2\frac{1}{5}\)
đ,125%.\(\left(\frac{1}{2}\right)^2:\left(1\frac{5}{6}-1,5\right)+2016^0\)
Bài 2 Tìm x biết
a,\(\left|\frac{3}{4}.x-\frac{1}{2}\right|=\frac{1}{4}\)
b, \(\frac{5}{3}.x-\frac{2}{5}.x=\frac{19}{10}\)
c, \(\left|2.x-\frac{1}{3}\right|=\frac{2}{9}\)
d, x-30%.x=-1\(\frac{1}{5}\)
Bài 1:
\(a,22\frac{1}{2}.\frac{7}{9}+50\%-1,25\)
=\(\frac{45}{2}.\frac{7}{9}+\frac{1}{2}-\frac{5}{4}\)
=\(\frac{35}{2}+\frac{1}{2}-\frac{5}{4}\)
=\(\frac{70}{4}+\frac{2}{4}-\frac{5}{4}\)
=\(\frac{67}{4}\)
\(b,1,4.\frac{15}{49}-\left(\frac{4}{5}+\frac{2}{3}\right):2\frac{1}{5}\)
=\(\frac{7}{5}.\frac{15}{49}-\left(\frac{12}{15}+\frac{10}{15}\right):\frac{11}{5}\)
=\(\frac{3}{7}-\frac{22}{15}.\frac{5}{11}\)
=\(\frac{3}{7}-\frac{2}{3}\)
=\(-\frac{5}{21}\)
\(c,125\%.\left(-\frac{1}{2}\right)^2:\left(1\frac{5}{6}-1,6\right)+2016^0\)
=\(\frac{5}{4}.\frac{1}{4}:\left(\frac{11}{6}-\frac{8}{5}\right)+1\)
=\(\frac{5}{16}:\frac{7}{30}+1\)
=\(\frac{131}{56}\)
\(d,1,4.\frac{15}{49}-\left(20\%+\frac{2}{3}\right):2\frac{1}{5}\)
=\(\frac{7}{5}.\frac{15}{49}-\left(\frac{1}{5}+\frac{2}{3}\right):\frac{11}{5}\)
=\(\frac{3}{7}-\frac{13}{15}:\frac{11}{5}\)
=\(\frac{3}{7}-\frac{13}{33}\)
=\(\frac{8}{231}\)
Bài đ làm giống hệt như bài c
Bài 2 :
\(a,\left|\frac{3}{4}.x-\frac{1}{2}\right|=\frac{1}{4}\)
=>\(\left[{}\begin{matrix}\frac{3}{4}.x-\frac{1}{2}=\frac{1}{4}\\\frac{3}{4}.x-\frac{1}{2}=-\frac{1}{4}\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}\frac{3}{4}.x=\frac{1}{4}+\frac{1}{2}=\frac{3}{4}\\\frac{3}{4}.x=-\frac{1}{4}+\frac{1}{2}=\frac{1}{4}\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=\frac{3}{4}:\frac{3}{4}=1\\x=\frac{1}{4}:\frac{3}{4}=\frac{1}{3}\end{matrix}\right.\)
Vậy x ∈{1;\(\frac{1}{3}\)}
\(b,\frac{5}{3}.x-\frac{2}{5}.x=\frac{19}{10}\)
=>\(\frac{19}{15}.x=\frac{19}{10}\)
=>\(x=\frac{19}{10}:\frac{19}{15}=\frac{3}{2}\)
Vậy x ∈ {\(\frac{3}{2}\)}
c,\(\left|2.x-\frac{1}{3}\right|=\frac{2}{9}\)
=>\(\left[{}\begin{matrix}2.x-\frac{1}{3}=\frac{2}{9}\\2.x-\frac{1}{3}=-\frac{2}{9}\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}2.x=\frac{2}{9}+\frac{1}{3}=\frac{5}{9}\\2.x=-\frac{2}{9}+\frac{1}{3}=\frac{1}{9}\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=\frac{5}{9}:2=\frac{5}{18}\\x=\frac{1}{9}:2=\frac{1}{18}\end{matrix}\right.\)
Vậy x∈{\(\frac{5}{18};\frac{1}{18}\)}
\(d,x-30\%.x=-1\frac{1}{5}\)
=\(70\%x=-\frac{6}{5}\)
=\(\frac{7}{10}.x=-\frac{6}{5}\)
=>\(x=-\frac{6}{5}:\frac{7}{10}=-\frac{12}{7}\)
Vậy x∈{\(-\frac{12}{7}\)}
Bài 2
a/
\(\Rightarrow\left[{}\begin{matrix}\frac{3}{4}.x-\frac{1}{2}=\frac{1}{4}\\\frac{3}{4}.x-\frac{1}{2}=-\frac{1}{4}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\frac{3}{4}.x=\frac{1}{4}+\frac{1}{2}\\\frac{3}{4}.x=-\frac{1}{4}+\frac{1}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\frac{3}{4}.x=\frac{3}{4}\\\frac{3}{4}.x=\frac{1}{4}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{3}{4}:\frac{3}{4}\\x=\frac{1}{4}:\frac{3}{4}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=\frac{1}{3}\end{matrix}\right.\)
Vậy \(x=1\) hoặc \(x=\frac{1}{3}\)
b/ Đặt x làm thừa số chung rồi tính như bình thường
c/ Tương tự câu a
d/ Tương tự câu b
a)22/1/2 .7/9 + 50% -1,25
=45/2 . 7/9 + 1/2 - 5/4
=35/2 +1/2 -5/4
= 18 - 5/4
=67/4
b)1,4 . 15/49- (4/5+ 2/3):2/1/5
=7/5 . 15/49 - (12/15 + 10/15) : 11/5
=3/7 - 22/15 : 11/5
=3/7 -2/3
=9/21 -14/21
=-5/21
c)125% . (-1/2)^2 : (1/5/6 - 1,6) + 2016^0
=5/4 . (-1/4) : (11/6- 8/5) +1
=-5/16 : (55/30 - 48/30 ) +1
=-5/16 :7/30 +1
=-75/56 + 1
= 131/56
d)1,4 .15/49 -(20% + 2/3) : 2/1/5
=7/5. 15/49 -(1/5 +2/3) :11/5
=3/7 - ( 3/15 +10/15) :11/5
=3/7 - 13/15 :11/5
=3/7 - 13/33
=8/231
đ)125%. (1/2)^2 : (1/5/6 - 1,5) +2016^0
=5/4 . 1/4 : (11/6 - 3/2)+1
=5/16 : 1/3 +1
=15/16 +1
=31/16
Rút gọn rồi tính giá trị của biểu thức:
A= \(\sqrt{\frac{\left(x-6^{ }\right)^4}{\left(5-x\right)^2}}+\frac{x^2-36}{x-5}\left(x< 5\right)\)tại x = \(\sqrt{\frac{12}{5}}:\sqrt{\frac{48}{5}}.\sqrt{64}\)
B= 5x - \(\sqrt{125}\) + \(\frac{\sqrt{x^3+5x^2}}{\sqrt{x+5}}\left(x>=0\right)\)tại x = \(\sqrt{\frac{65}{17}}:\sqrt{\frac{13}{4}}\)
C= \(\sqrt{\frac{\left(x-2\right)^4}{\left(3-x\right)^2}}+\frac{\sqrt{x^4-2x^2+1}}{x-3}\left(x< 3\right)\)tại x =\(\sqrt{\frac{1}{18}}:\frac{1}{\sqrt{81}}\)
Các bác giúp e vs ạ, hứa sẽ tick, e cảm ơn nhiều!!!!!!!!
Bài 1: Rút gọn biểu thức
\(A=\frac{2^{10}.13+2^{10}.65}{2^8.104}\) \(B=\frac{15.3^{11}+4.27^4}{9^7}\) \(C=\left(125^3.7^5-175^5:5\right):2016^{2017}\)
Bài 2: Tìm x:
a)\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{x.\left(x+3\right)}=\frac{6}{19}\)b)\(\left|\frac{3}{13}x^2+\frac{1}{2}\right|-\frac{3}{4}=\frac{5}{6}\)
Bài 1: Rút gọn biểu thức
\(A=\frac{2^{10}.13+2^{10}.65}{2^8.104}\) \(B=\frac{15.3^{11}+4.27^4}{9^7}\) \(C=\left(125^3.7^5-175^5:5\right):2016^{2017}\)
Bài 2: Tìm x:
a)\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{x.\left(x+3\right)}=\frac{6}{19}\)b)\(\left|\frac{3}{13}x^2+\frac{1}{2}\right|-\frac{3}{4}=\frac{5}{6}\)
Bài 1: Tìm n
1/4*2/6*3/8*4/10*5/12*.....* 30/62*31/64=2^n
Bài 2: Tính
a) \(\frac{\left(-5\right)^{60}\cdot30^5}{15^5\cdot5^{61}}\)
b)\(2^3+3\cdot\left(\frac{1}{3}\right)^0-2^{-2}\cdot4+\left[\left(-2\right)^3:\frac{1}{2}\right]\cdot8\)
(GỢI Ý CÂU B:\(^{2^{-2}=\frac{1}{2^2}}\)
Bài 3: Tìm x
a)\(^{2^x=16}\)
b)\(^{\left(\frac{x}{13}\right)^2=\frac{49}{169}}\)
c)\(\left(\frac{-1}{5}\right)^x=\left(\frac{-1}{125}\right)^3\cdot x^4=\frac{-16}{625}\)
d)\(^{6^{4-x}=216}\)
Bài 4:Tìm n
a)\(3^n\cdot3^{-2}=3^5\)
b)Tìm x:
1)\(\frac{2^{4-x}}{16^5}=32^6\)
2)\(^{9\cdot5^x=6\cdot5^6+3\cdot5^6}\)
3)\(\frac{2^3}{2^x}=4^5\)
Các bạn giúp mik!!!Mik sắp kiểm tra 45p r