\(\dfrac{2\cdot3\cdot5^2}{3^2\cdot5^3}\)

\(=2\cdot\dfrac{3}{3^2}\cdot\dfrac{5^2}{5^3}\)

\(=2\cdot\dfrac{1}{3}\cdot\dfrac{1}{5}\)

\(=\dfrac{2}{15}\)

\(\dfrac{2.3.5^2}{3^2.5^2}=\dfrac{2}{3}\)

x^{Lập phương} = x³

x^{Bình phương} = x²

bình phương = x²

lập phương = x³

17 - 8 = 9

17-8=9 

Tính hợp lí: 

a) \(\left(-0,4\right)+\dfrac{3}{8}+\left(-0,6\right)\)

\(=\left[\left(-0,4\right)+\left(-0,6\right)\right]+\dfrac{3}{8}\)

\(=-1+\dfrac{3}{8}\)

\(=\dfrac{\left(-8\right)+3}{8}\)

\(=\dfrac{-5}{8}\)

b) \(\dfrac{4}{5}-1,8+0,375+\dfrac{5}{8}\)

\(=\dfrac{4}{5}-\dfrac{9}{5}+\dfrac{3}{8}+\dfrac{5}{8}\)

\(=-1+1\)

\(=0\\\)

c) \(\dfrac{7}{3}.\left(-2,5\right).\dfrac{6}{7}\)

\(=\dfrac{7}{3}.\dfrac{-5}{2}.\dfrac{6}{7}\)

\(=\dfrac{7}{3}.\dfrac{6}{7}.\dfrac{-5}{2}\)

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

\(=-5\)

d) \(\dfrac{7}{12}.\left(-2,34\right)-\dfrac{7}{12}.\left(-0,34\right)\)

\(=\dfrac{7}{12}.\left[\left(-2,34\right)+0,34\right]\)

\(=\dfrac{7}{12}.\left(-2\right)\)

\(=\dfrac{-7}{6}\)

e) \(\dfrac{-8}{3}.\dfrac{2}{11}-\dfrac{8}{3}:\dfrac{11}{9}\)

\(=\dfrac{8}{3}.\dfrac{-2}{11}-\dfrac{8}{3}.\dfrac{9}{11}\)

\(=\dfrac{8}{3}.\left(\dfrac{-2}{11}-\dfrac{9}{11}\right)\)

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

\(=\dfrac{-8}{3}\)

Chúc bạn học tốt

Cảm ơn nha.

Từ 100 đến 2023 có : (2023-100+1):2= 962 số tự nhiên là số chẵn.

Ta có số tự nhiên chăn nhỏ nhất trong khoảng đó là 100

Và số lớn nhất là 2022

Số lượng số tự nhiên chẵn có trong khoảng đó là:

\(\left(2022-100\right):2+1=962\) (số)

Các phần tử của tập hợp A là:

\(A=\left\{10;11;12;...;99\right\}\)

Số lượng phần tử:

\(\left(99-10\right):1+1=90\) (phần tử)

Các phần tử của tập hợp A là:

$A=\left\{10;11;12;...;99\right\}$

Số lượng phần tử:

$\left(99-10\right):1+1=90$ (phần tử)

\(\dfrac{5}{4}+\left(2x-\dfrac{1}{2}\right)=\dfrac{5}{6}\\ =>2x-\dfrac{1}{2}=\dfrac{5}{6}-\dfrac{5}{4}\\ =>2x-\dfrac{1}{2}=\dfrac{10}{12}-\dfrac{15}{12}\\ =>2x-\dfrac{1}{2}=-\dfrac{5}{12}\\ =>2x=-\dfrac{5}{12}+\dfrac{1}{2}\\ =>2x=-\dfrac{5}{12}+\dfrac{6}{12}\\ =>2x=\dfrac{1}{12}\\ =>x=\dfrac{1}{12}:2\\ =>x=\dfrac{1}{12}\cdot\dfrac{1}{2}\\ =>x=\dfrac{1}{24}\)

__

\(\dfrac{3}{2}-\left(x+\dfrac{1}{4}\right)=\dfrac{5}{8}\\ =>x+\dfrac{1}{4}=\dfrac{3}{2}-\dfrac{5}{8}\\ =>x+\dfrac{1}{4}=\dfrac{12}{8}-\dfrac{5}{8}\\ =>x+\dfrac{1}{4}=\dfrac{7}{8}\\ =>x=\dfrac{7}{8}-\dfrac{1}{4}\\ =>x=\dfrac{7}{8}-\dfrac{2}{8}\\ =>x=\dfrac{5}{8}\)

__

\(\dfrac{x}{3}=\dfrac{12}{x}\\ =>x^2=3\cdot12\\ =>x^2=36\\ =>x^2=6^2\\ =>x=\pm6\)

Tìm x: 

a) \(\dfrac{5}{4}+\left(2x-\dfrac{1}{2}\right)=\dfrac{5}{6}\)

\(=>2x-\dfrac{1}{2}=\dfrac{5}{6}-\dfrac{5}{4}\)

\(=>2x-\dfrac{1}{2}=\dfrac{-5}{12}\)

\(=>2x=\dfrac{-5}{12}+\dfrac{1}{2}\)

\(=>2x=\dfrac{1}{12}\)

\(=>x=\dfrac{1}{12}:2\)

\(=>x=\dfrac{1}{24}\)

b) \(\dfrac{3}{2}-\left(x+\dfrac{1}{4}\right)=\dfrac{5}{8}\)

\(=>x+\dfrac{1}{4}=\dfrac{3}{2}-\dfrac{5}{8}\)

\(=>x+\dfrac{1}{4}=\dfrac{7}{8}\)

\(=>x=\dfrac{7}{8}-\dfrac{1}{4}\)

\(=>x=\dfrac{5}{8}\)

c) \(\dfrac{x}{3}=\dfrac{12}{x}\)

Ta có: \(x.x=3.12\)

\(\Rightarrow x^2=36\)

Vậy x = 6 hoặc x = -6

Chúc bạn học tốt

1. Tính hợp lí

a) \(0,7+\dfrac{-7}{19}-\left(-0,3\right)\)

\(=\dfrac{7}{10}+\dfrac{-7}{19}+\dfrac{3}{10}\)

\(=\left(\dfrac{7}{10}+\dfrac{3}{10}\right)+\dfrac{-7}{19}\)

\(=1+\dfrac{-7}{19}\)

\(=\dfrac{12}{19}\)

b) \(\dfrac{5}{3}.\left(-2,5\right):\dfrac{5}{6}\)

\(=\dfrac{5}{3}.\dfrac{-5}{2}.\dfrac{6}{5}\)

\(=\left(\dfrac{5}{3}.\dfrac{6}{5}\right).\dfrac{-5}{2}\)

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

\(=-5\)

c) \(0,6.\dfrac{-5}{17}-\dfrac{3}{5}.\dfrac{12}{17}\)

\(=\dfrac{3}{5}.\dfrac{-5}{17}-\dfrac{3}{5}.\dfrac{12}{17}\)

\(=\dfrac{3}{5}.\left(\dfrac{-5}{17}-\dfrac{12}{17}\right)\)

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

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

d) \(\dfrac{7}{4}.\dfrac{5}{2}-\dfrac{7}{4}.\dfrac{3}{2}\)

\(=\dfrac{7}{4}.\left(\dfrac{5}{2}-\dfrac{3}{2}\right)\)

\(=\dfrac{7}{4}.1\)

\(=\dfrac{7}{4}\)

Chúc bạn học tốt

a) $0,7+\genfrac{}{}{0ex}{}{-7}{19}-\left(-0,3\right)$

$=\genfrac{}{}{0ex}{}{7}{10}+\genfrac{}{}{0ex}{}{-7}{19}+\genfrac{}{}{0ex}{}{3}{10}$

$=\left(\genfrac{}{}{0ex}{}{7}{10}+\genfrac{}{}{0ex}{}{3}{10}\right)+\genfrac{}{}{0ex}{}{-7}{19}$

$=1+\genfrac{}{}{0ex}{}{-7}{19}$

$=\genfrac{}{}{0ex}{}{12}{19}$

b) $\genfrac{}{}{0ex}{}{5}{3}.\left(-2,5\right):\genfrac{}{}{0ex}{}{5}{6}$

$=\genfrac{}{}{0ex}{}{5}{3}.\genfrac{}{}{0ex}{}{-5}{2}.\genfrac{}{}{0ex}{}{6}{5}$

$=\left(\genfrac{}{}{0ex}{}{5}{3}.\genfrac{}{}{0ex}{}{6}{5}\right).\genfrac{}{}{0ex}{}{-5}{2}$

$=2.\genfrac{}{}{0ex}{}{-5}{2}$

$=-5$

c) $0,6.\genfrac{}{}{0ex}{}{-5}{17}-\genfrac{}{}{0ex}{}{3}{5}.\genfrac{}{}{0ex}{}{12}{17}$

$=\genfrac{}{}{0ex}{}{3}{5}.\genfrac{}{}{0ex}{}{-5}{17}-\genfrac{}{}{0ex}{}{3}{5}.\genfrac{}{}{0ex}{}{12}{17}$

$=\genfrac{}{}{0ex}{}{3}{5}.\left(\genfrac{}{}{0ex}{}{-5}{17}-\genfrac{}{}{0ex}{}{12}{17}\right)$

$=\genfrac{}{}{0ex}{}{3}{5}.-1$

$=\genfrac{}{}{0ex}{}{-3}{5}$

d) $\genfrac{}{}{0ex}{}{7}{4}.\genfrac{}{}{0ex}{}{5}{2}-\genfrac{}{}{0ex}{}{7}{4}.\genfrac{}{}{0ex}{}{3}{2}$

$=\genfrac{}{}{0ex}{}{7}{4}.\left(\genfrac{}{}{0ex}{}{5}{2}-\genfrac{}{}{0ex}{}{3}{2}\right)$

$=\genfrac{}{}{0ex}{}{7}{4}.1$

$=\genfrac{}{}{0ex}{}{7}{4}$

mình giúp rùi đó nhớ tick mình nha

\(\dfrac{1}{3}-\dfrac{1}{12}-\dfrac{1}{20}-\dfrac{1}{30}-\dfrac{1}{42}-\dfrac{1}{56}-\dfrac{1}{72}-\dfrac{1}{90}-\dfrac{1}{110}=x-\dfrac{5}{13}\)

\(\dfrac{1}{3}\) - \(\dfrac{1}{3.4}\) - \(\dfrac{1}{4.5}\) - \(\dfrac{1}{5.6}\) - \(\dfrac{1}{6.7}\) - \(\dfrac{1}{7.8}\)- \(\dfrac{1}{8.9}\) - \(\dfrac{1}{9.10}\) - \(\dfrac{1}{10.11}\) = \(x\) - \(\dfrac{5}{13}\)

\(\dfrac{1}{3}\) - (\(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\) + \(\dfrac{1}{6.7}\)+ \(\dfrac{1}{7.8}\) + \(\dfrac{1}{8.9}\) + \(\dfrac{1}{9.10}\) + \(\dfrac{1}{10.11}\) =\(x\)-\(\dfrac{5}{13}\)

\(\dfrac{1}{3}\)  - (\(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) +...+ \(\dfrac{1}{9}\) - \(\dfrac{1}{10}\) + \(\dfrac{1}{10}\) - \(\dfrac{1}{11}\)) = \(x\) - \(\dfrac{5}{13}\)

 \(\dfrac{1}{3}\) - (\(\dfrac{1}{3}\) - \(\dfrac{1}{11}\)) =  \(x\) - \(\dfrac{5}{13}\)

\(\dfrac{1}{3}\) - \(\dfrac{1}{3}\) +  \(\dfrac{1}{11}\) =  \(x\) - \(\dfrac{5}{13}\)

         \(x-\dfrac{5}{13}=\dfrac{1}{11}\)

        \(x\)           = \(\dfrac{1}{11}\) + \(\dfrac{5}{13}\)

      \(x\)           = \(\dfrac{68}{143}\)

Em cảm ơn ạ.

`@` `\text {Ans}`

`\downarrow`

`82.8^n=41984`

`=> 8^n = 41984 \div 82`

`=> 8^n = 512`

`=> 8^n = 8^3`

`=> n=3`

Vậy, `n = 3`.

giúp tớ với ❤