Question-197393

Question Number 197393 by mathlove last updated on 16/Sep/23

Answered by Frix last updated on 16/Sep/23

((3×5((2^2 ((2^6 3))^(1/3) ))^(1/3) +3×7((2×3^2 (3^4 )^(1/3) ))^(1/3) )/( ((2^2 3((2^3 3))^(1/3) +2×3((3×5^3 ))^(1/3) ))^(1/3) ))= =((2^(4/3) 3^((10)/9) 5+2^(1/3) 3^((19)/9) 7)/((2^3 3^(4/3) +2×3^(4/3) 5)^(1/3) ))=((2^(1/3) 3^((10)/9) (2×5+3×7))/((2×3^(4/3) (4+5))^(1/3) ))= =((2^(1/3) 3^((10)/9) 31)/(2^(1/3) 3^((10)/9) ))=31

$$\frac{\mathrm{3}×\mathrm{5}\sqrt[{\mathrm{3}}]{\mathrm{2}^{\mathrm{2}} \sqrt[{\mathrm{3}}]{\mathrm{2}^{\mathrm{6}} \mathrm{3}}}+\mathrm{3}×\mathrm{7}\sqrt[{\mathrm{3}}]{\mathrm{2}×\mathrm{3}^{\mathrm{2}} \sqrt[{\mathrm{3}}]{\mathrm{3}^{\mathrm{4}} }}}{\:\sqrt[{\mathrm{3}}]{\mathrm{2}^{\mathrm{2}} \mathrm{3}\sqrt[{\mathrm{3}}]{\mathrm{2}^{\mathrm{3}} \mathrm{3}}+\mathrm{2}×\mathrm{3}\sqrt[{\mathrm{3}}]{\mathrm{3}×\mathrm{5}^{\mathrm{3}} }}}= \\ $$$$=\frac{\mathrm{2}^{\frac{\mathrm{4}}{\mathrm{3}}} \mathrm{3}^{\frac{\mathrm{10}}{\mathrm{9}}} \mathrm{5}+\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{3}}} \mathrm{3}^{\frac{\mathrm{19}}{\mathrm{9}}} \mathrm{7}}{\left(\mathrm{2}^{\mathrm{3}} \mathrm{3}^{\frac{\mathrm{4}}{\mathrm{3}}} +\mathrm{2}×\mathrm{3}^{\frac{\mathrm{4}}{\mathrm{3}}} \mathrm{5}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} }=\frac{\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{3}}} \mathrm{3}^{\frac{\mathrm{10}}{\mathrm{9}}} \left(\mathrm{2}×\mathrm{5}+\mathrm{3}×\mathrm{7}\right)}{\left(\mathrm{2}×\mathrm{3}^{\frac{\mathrm{4}}{\mathrm{3}}} \left(\mathrm{4}+\mathrm{5}\right)\right)^{\frac{\mathrm{1}}{\mathrm{3}}} }= \\ $$$$=\frac{\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{3}}} \mathrm{3}^{\frac{\mathrm{10}}{\mathrm{9}}} \mathrm{31}}{\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{3}}} \mathrm{3}^{\frac{\mathrm{10}}{\mathrm{9}}} }=\mathrm{31} \\ $$

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