Question

3. Ordonați crescător: 8.96 + (92)3; (53)4.25; 417:213.
Va rog sa m-a ajutați!!
Dau stea!

Answer 1

Răspuns: $\green{\bf \green{8^{7}~<~9^7~<~25^7}~}$

Explicație pas cu pas:

Cerința corecta: "Ordonați crescător: 8 × 9⁶ + (9²)³ ; (5³)⁴ × 25 ; 4¹⁷ : 2¹³"

$\bf 8\cdot 9^{6}+(9^2)^3=8\cdot 9^{6}+9^{2\cdot3}=$

$\bf 8\cdot 9^{6}+9^{6}=9^{6}\cdot (8\cdot 9^{6-6}+9^{6-6})=$

$\bf 9^{6}\cdot (8\cdot 9^{0}+9^{0})=9^{6}\cdot (8\cdot1+1)=$

$\bf 9^{6}\cdot9=9^{6+1}=\purple{\underline{9^{7}}}$

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$\bf (5^3)^4\cdot 25=5^{3\cdot4}\cdot 5^2=5^{12}\cdot 5^2=$

$\bf 5^{12+2}=5^{14} =(5^{2})^7=\pink{\underline{25^{7}}}$

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$\bf 4^{17}:2^{13}=(2^2)^{17}:2^{13}=2^{2\cdot17}:2^{13}=$

$\bf 2^{34}:2^{13}=2^{34-13}=2^{21}=$

$\bf (2^{3})^7=\red{\underline{8^{7}}}$

============================

$\green{\bf \green{8^{7}~<~9^7~<~25^7}~}$

Bafta multa !