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Bài 1:
\(\text{a) }x.x^2.x^3.x^4.x^5.....x^{49}.x^{50}\)
\(=x^{1+2+3+4+5+...+49+50}\)
\(=x^{\frac{51.50}{2}}\)
\(=x^{1275}\)
\(\text{b) Ta có:}\)
\(4^{15}=\left(2^2\right)^{15}=2^{2.15}=2^{30}\)
\(8^{11}=\left(2^3\right)^{11}=2^{3.11}=2^{33}\)
\(\text{Vì }2^{30}< 2^{33}\text{ nên }4^{15}< 8^{11}\)
Bài 2: Tìm x
\(\left(x-1\right)^4:3^2=3^6\)
\(\Rightarrow\left(x-1\right)^4=3^6\times3^2\)
\(\Rightarrow\left(x-1\right)^4=3^8\)
\(\Rightarrow\left(x-1\right)^4=3^{2.4}\)
\(\Rightarrow\left(x-1\right)^4=\left(3^2\right)^4\)
\(\Rightarrow x-1=9\)
\(\Rightarrow x=10\)
Bài 3 và bài 4 mk làm sau
Bài 1 : a) \(x.x^2.x^3.x^4.....x^{49}.x^{50}=x^{1+2+3+...+49+50}\) (Dễ rồi tự tính)
b) \(\hept{\begin{cases}4^{15}=\left(2^2\right)^{15}=2^{30}\\8^{11}=\left(2^3\right)^{11}=2^{33}\end{cases}}\)Rồi tự so sánh đi
Bài 2 :
\(\left(x-1\right)^4\div3^2=3^6\Leftrightarrow\left(x-1\right)^4=3^8=\left(3^2\right)^4=9^4\Leftrightarrow x-1=9\Leftrightarrow x=10\)
Bài 3 :
\(\hept{\begin{cases}27^{15}=\left(3^3\right)^{15}=3^{45}\\81^{11}=\left(3^4\right)^{11}=3^{44}\end{cases}}\) nt
\(a;\dfrac{2}{3}x-50\%x-\left(-\dfrac{4}{5}\right):1\dfrac{3}{5}=-0,12+1\dfrac{3}{25}\\ \dfrac{1}{6}x+\dfrac{1}{2}=1\Rightarrow\dfrac{1}{6}x=1-\dfrac{1}{2}=\dfrac{1}{2}\\ \Rightarrow x=\dfrac{1}{2}:\dfrac{1}{6}=3\\ b;\left(-1\dfrac{1}{6}+\dfrac{2}{3}-\dfrac{3}{4}\right):x+\left(-1\dfrac{11}{12}\right)\cdot1\dfrac{21}{23}=-6\dfrac{1}{3}\\ -\dfrac{5}{4}:x-\dfrac{11}{3}=-\dfrac{19}{3}\\ -\dfrac{5}{4}:x=-\dfrac{19}{3}+\dfrac{11}{3}=-\dfrac{8}{3}\\ x=-\dfrac{5}{4}:\left(-\dfrac{8}{3}\right)=\dfrac{15}{32}\\ c;50\%x-\dfrac{1}{3}x-\left(-\dfrac{2}{3}\right)^2\cdot\left(-1\dfrac{1}{8}\right)=-119\dfrac{3}{4}+120\dfrac{5}{6}\\ \dfrac{1}{6}x+\dfrac{1}{2}=\dfrac{13}{12}\Rightarrow\dfrac{1}{6}x=\dfrac{13}{12}-\dfrac{1}{2}=\dfrac{7}{12}\\ x=\dfrac{7}{12}:\dfrac{1}{6}=\dfrac{7}{2}\)
a) \(x-\frac{5}{7}=\frac{1}{9}\Rightarrow x=\frac{1}{9}+\frac{5}{7}\Rightarrow x=\frac{52}{63}\)
b) \(\frac{-3}{7}-x=\frac{4}{5}+\frac{-2}{3}\Rightarrow\frac{-3}{7}-x=\frac{2}{15}\Rightarrow x=\frac{-3}{7}-\frac{2}{15}\Rightarrow x=\frac{-59}{105}\)
c) \(x-\frac{1}{5}=\frac{2}{7}.\frac{-11}{5}\Rightarrow x-\frac{1}{5}=\frac{-22}{35}\Rightarrow x=\frac{-22}{35}+\frac{1}{5}\Rightarrow x=\frac{-3}{7}\)
d) \(\frac{x}{182}=\frac{-6}{14}.\frac{35}{91}\Rightarrow\frac{x}{182}=\frac{-15}{91}\Rightarrow x=\frac{\left(-15\right).182}{91}\Rightarrow x=-30\)
a)\(\left(\frac{3}{29}-\frac{1}{5}\right)\cdot\frac{29}{3}\)
\(=\left(\frac{3}{29}\cdot\frac{29}{3}\right)-\left(\frac{1}{5}\cdot\frac{29}{3}\right)\)
\(=1-\frac{29}{15}\)
\(=\frac{-14}{15}\)
b)\(\frac{16}{15}\cdot\frac{-5}{14}\cdot\frac{54}{24}\cdot\frac{56}{21}\)
=\(=\frac{16\cdot\left(-5\right)\cdot54\cdot56}{15\cdot14\cdot24\cdot21}\)
\(=\frac{2^4\cdot\left(-5\right)\cdot2\cdot3^3\cdot2^3\cdot7}{3\cdot5\cdot7\cdot2\cdot2^3\cdot3\cdot7}\)
\(=2^4\)
c)\(\frac{37}{7}\cdot\frac{8}{11}+\frac{37}{7}\cdot\frac{5}{11}-\frac{37}{7}\cdot\frac{2}{11}\)
\(=\frac{37}{7}\cdot\left(\frac{8}{11}+\frac{5}{11}-\frac{2}{11}\right)\)
\(=\frac{37}{7}\cdot1\)
\(=\frac{37}{7}\)
Đúng nhớ k nhen!
a: \(\Leftrightarrow\dfrac{8}{5}+\dfrac{2}{5}\cdot x=\dfrac{16}{5}\)
=>2/5x=8/5
=>x=4
b: \(\Leftrightarrow\left(\dfrac{1}{24}-\dfrac{1}{25}+\dfrac{1}{25}-\dfrac{1}{26}+...+\dfrac{1}{39}-\dfrac{1}{40}\right)\cdot120+\dfrac{1}{3}x=-4\)
\(\Leftrightarrow x\cdot\dfrac{1}{3}+2=-4\)
=>1/3x=-6
=>x=-18
c: =>2|x-1/3|=0,24-4/5=-0,56<0
`a)x + 37 = 50`
`=> x = 50 -37`
`=> x = 13`
Vậy `x =13`
`b) 2x -3 = 11`
`=> 2x =11 +3`
`=> 2x = 14`
`=> x = 14 :2`
`=> x = 7`
Vậy `x =7`
`c) (6-x) :2 = 5`
`=> 6-x = 5 xx2`
`=> 6-x = 10`
`=> x = 6-10`
`=> x = -4`
Vậy `x =-4`