\(10+2\cdot x=4^5:4^3\)

\(\Rightarrow10+2\cdot x=4^{5-3}\)

\(\Rightarrow10+2\cdot x=4^2\)

\(\Rightarrow10+2\cdot x=16\)

\(\Rightarrow2\cdot x=16-10\)

\(\Rightarrow2\cdot x=6\)

\(\Rightarrow x=\dfrac{6}{2}=3\)

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\(2\cdot x-6^2:18=3\cdot2^2\)

\(\Rightarrow2\cdot x-36:18=12\)

\(\Rightarrow2\cdot x-2=12\)

\(\Rightarrow2\cdot x=12+2\)

\(\Rightarrow2\cdot x=14\)

\(\Rightarrow x=\dfrac{14}{2}=7\)

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\(70-5\cdot\left(x-3\right)=3\cdot2\)

\(\Rightarrow70-5\cdot\left(x-3\right)=6\)

\(\Rightarrow70-5x+15=6\)

\(\Rightarrow-5x+15=6-70\)

\(\Rightarrow-5x+15=64\)

\(\Rightarrow-5x=64-15\)

\(\Rightarrow-5x=49\)

\(\Rightarrow x=-\dfrac{49}{5}\)

\(5\cdot4^2-18:3^2\)

\(=5\cdot16-18:9\)

\(=80-2\)

\(=78\)

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\(6^2:4\cdot3+2\cdot5^3\)

\(=36:12+2\cdot125\)

\(=3+250\)

\(=253\)

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\(80-\left(4\cdot5^2-3\cdot2^3\right)\)

\(=80-\left(4\cdot25-3\cdot8\right)\)

\(=80-\left(100-24\right)\)

\(=80-76\)

\(=4\)

\(74\left(x-3\right)=0\)

\(\Rightarrow x-3=0\)

\(\Rightarrow x=3\)

a) \(A=\left(-0,75-\dfrac{1}{4}\right):\left(-5\right)+\dfrac{1}{48}-\left(-\dfrac{1}{6}\right):\left(-3\right)\)

\(A=\left(-0,75-0,25\right):\left(-5\right)+\dfrac{1}{48}-\left(-\dfrac{1}{6}\right)\cdot\dfrac{-1}{3}\)

\(A=\left(-1\right):\left(-5\right)+\dfrac{1}{48}-\dfrac{1}{18}\)

\(A=\dfrac{1}{5}+\dfrac{1}{48}-\dfrac{1}{18}\)

\(A=\dfrac{119}{720}\)

b) \(B=\left(\dfrac{6}{25}-1,24\right):\dfrac{3}{7}:\left[\left(3\dfrac{1}{2}-3\dfrac{2}{3}\right):\dfrac{1}{14}\right]\)

\(B=\left(0,24-1,24\right):\dfrac{3}{7}:\left[\left(\dfrac{7}{2}-\dfrac{11}{3}\right):\dfrac{1}{14}\right]\)

\(B=-1:\dfrac{3}{7}:\left(-\dfrac{1}{6}:\dfrac{1}{14}\right)\)

\(B=-\dfrac{7}{3}:-\dfrac{7}{3}\)

\(B=1\)

\(5\times\dfrac{6}{3}\)

\(=5\times2\)

\(=10\)

\(6+4\cdot x=38+16\)

\(\Rightarrow6+4\cdot x=54\)

\(\Rightarrow4\cdot x=54-6\)

\(\Rightarrow4\cdot x=48\)

\(\Rightarrow x=\dfrac{48}{4}=12\)

\(\dfrac{1}{20}-\left(x-\dfrac{8}{5}\right)=\dfrac{1}{10}\)

\(\Rightarrow\dfrac{1}{20}-x+\dfrac{8}{5}=\dfrac{1}{10}\)

\(\Rightarrow\dfrac{33}{20}-x=\dfrac{1}{10}\)

\(\Rightarrow x=\dfrac{33}{20}-\dfrac{1}{10}\)

\(\Rightarrow x=\dfrac{31}{20}\)

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\(\dfrac{16}{5}-x=\dfrac{4}{5}-\dfrac{3}{10}\)

\(\Rightarrow\dfrac{16}{5}-x=\dfrac{1}{2}\)

\(\Rightarrow x=\dfrac{16}{5}-\dfrac{1}{2}\)

\(\Rightarrow x=\dfrac{27}{10}\)

a) \(4\cdot8=2^2\cdot2^3\)

\(=2^{2+3}=2^5=32\)

b) \(4^5\cdot4^4\cdot4\)

\(=4^{5+4+1}=4^{10}\)

c) \(x^5\cdot x\)

\(=x^{5+1}=x^6\)

d) \(9\cdot27=3^2\cdot3^3\)

\(=3^{2+3}=3^5\)

e) \(243:81=3^5:3^4\)

\(=3^{5-4}=3^1=3\)

g) \(625:25=5^4:5^2\)

\(=5^{4-2}=5^2=25\)

Trong 1 giờ vòi 1 chảy được:

\(1:10=\dfrac{1}{10}\)(bể)

Trong 1 giờ vòi thứ hai chảy được:

\(1:8=\dfrac{1}{8}\) (bể)

Hai vòi chảy cùng lúc thì trong 1 giờ chảy được:

\(\dfrac{1}{10}+\dfrac{1}{8}=\dfrac{9}{40}\) (bể)

Vậy hai vòi muốn chảy đầy bể thì mất:

\(1:\dfrac{9}{40}=\dfrac{40}{9}\) (giờ)

Đáp số: ...

Liệt kê:

\(A=\left\{0;1;2;3;4;5;6;7;8;9;10;11;12\right\}\)