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Question Number 202796 by MathematicalUser2357 last updated on 03/Jan/24

[2^(8÷2−1) +4÷{2+2^(4÷(1+1)) ÷(6÷3−1)}]÷[6÷{(3^(4÷2) +5÷5)÷2−6÷(5−2)}]

$$\left[\mathrm{2}^{\mathrm{8}\boldsymbol{\div}\mathrm{2}−\mathrm{1}} +\mathrm{4}\boldsymbol{\div}\left\{\mathrm{2}+\mathrm{2}^{\mathrm{4}\boldsymbol{\div}\left(\mathrm{1}+\mathrm{1}\right)} \boldsymbol{\div}\left(\mathrm{6}\boldsymbol{\div}\mathrm{3}−\mathrm{1}\right)\right\}\right]\boldsymbol{\div}\left[\mathrm{6}\boldsymbol{\div}\left\{\left(\mathrm{3}^{\mathrm{4}\boldsymbol{\div}\mathrm{2}} +\mathrm{5}\boldsymbol{\div}\mathrm{5}\right)\boldsymbol{\div}\mathrm{2}−\mathrm{6}\boldsymbol{\div}\left(\mathrm{5}−\mathrm{2}\right)\right\}\right] \\ $$

Answered by a.lgnaoui last updated on 03/Jan/24

si ( (./.)) est une operation de[division ⇒ Expression est equivalente a X=[A+(4/(2+(B/C)))]×(((D−E)/6)) A=2^3 =8 (B/C)=(2^2 /1)=4 D−E=((3^2 +1)/2)−(6/3)=5−2=3 ⇒ X=(8+(4/(2+4)))×((3/6))=(8+(2/3))×(1/2) X=((13)/3)

$$\mathrm{si}\:\left(\:\frac{.}{.}\right)\:\:\mathrm{est}\:\mathrm{une}\:\mathrm{operation}\:\mathrm{de}\left[\mathrm{division}\right. \\ $$$$\:\:\Rightarrow\:\mathrm{Expression}\:\mathrm{est}\:\mathrm{equivalente}\:\mathrm{a} \\ $$$$\:\:\:\boldsymbol{\mathrm{X}}=\left[\mathrm{A}+\frac{\mathrm{4}}{\mathrm{2}+\frac{\mathrm{B}}{\mathrm{C}}}\right]×\left(\frac{\mathrm{D}−\mathrm{E}}{\mathrm{6}}\right) \\ $$$$\mathrm{A}=\mathrm{2}^{\mathrm{3}} =\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{B}}{\mathrm{C}}=\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{1}}=\mathrm{4}\:\:\:\: \\ $$$$\:\mathrm{D}−\mathrm{E}=\frac{\mathrm{3}^{\mathrm{2}} +\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{6}}{\mathrm{3}}=\mathrm{5}−\mathrm{2}=\mathrm{3} \\ $$$$\Rightarrow\:\mathrm{X}=\left(\mathrm{8}+\frac{\mathrm{4}}{\mathrm{2}+\mathrm{4}}\right)×\left(\frac{\mathrm{3}}{\mathrm{6}}\right)=\left(\mathrm{8}+\frac{\mathrm{2}}{\mathrm{3}}\right)×\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{X}}=\frac{\mathrm{13}}{\mathrm{3}} \\ $$

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