Răspuns: [tex]\green{\bf \green{8^{7}~<~9^7~<~25^7}~}[/tex]
Explicație pas cu pas:
Cerința corecta: "Ordonați crescător: 8 × 9⁶ + (9²)³ ; (5³)⁴ × 25 ; 4¹⁷ : 2¹³"
[tex]\bf 8\cdot 9^{6}+(9^2)^3=8\cdot 9^{6}+9^{2\cdot3}=[/tex]
[tex]\bf 8\cdot 9^{6}+9^{6}=9^{6}\cdot (8\cdot 9^{6-6}+9^{6-6})=[/tex]
[tex]\bf 9^{6}\cdot (8\cdot 9^{0}+9^{0})=9^{6}\cdot (8\cdot1+1)=[/tex]
[tex]\bf 9^{6}\cdot9=9^{6+1}=\purple{\underline{9^{7}}}[/tex]
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[tex]\bf (5^3)^4\cdot 25=5^{3\cdot4}\cdot 5^2=5^{12}\cdot 5^2=[/tex]
[tex]\bf 5^{12+2}=5^{14} =(5^{2})^7=\pink{\underline{25^{7}}}[/tex]
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[tex]\bf 4^{17}:2^{13}=(2^2)^{17}:2^{13}=2^{2\cdot17}:2^{13}=[/tex]
[tex]\bf 2^{34}:2^{13}=2^{34-13}=2^{21}=[/tex]
[tex]\bf (2^{3})^7=\red{\underline{8^{7}}}[/tex]
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[tex]\green{\bf \green{8^{7}~<~9^7~<~25^7}~}[/tex]
Bafta multa !
