Question

Simplificati fractiile 8^25/16^2,4^26/32^11, 9^17/3^37, 27^30/3^91,81^19/9^39.
Va rog sa ma ajute cineva pana la ora 19:00, daca se poate!Dau cotoana si 30 de puncte! ​

Answer 1

Răspuns:

Explicație pas cu pas:

8²⁵/ 16² = (2³)²⁵/(2⁴)² = 2⁽³ˣ²⁵⁾ / 2⁽⁴ˣ²⁾ = 2⁷⁵/2⁸ = 2⁽⁷⁵⁻⁸⁾ = 2⁶⁷

-  se simplifică cu 2⁸

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4²⁶/32¹¹ = (2²)²⁶ / (2⁵)¹¹ = 2⁽²ˣ²⁶⁾ / 2⁽⁵ˣ¹¹⁾ = 2⁵²/2⁵⁵ = 1/2³ = 1/8

- se simplifică cu 2⁵² (2⁵²:2⁵²)/(2⁵⁵:2⁵²) = 1/2⁽⁵⁵⁻⁵²⁾ = 1/2³

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9¹⁷/3³⁷ = (3²)¹⁷ /3³⁷ = 3⁽²ˣ¹⁷⁾/3³⁷ = 3³⁴/3³⁷= (3³⁴/3³⁴) x (1/3³) = 1/3³ = 1/27

-  se simplifică cu 3³⁴ :  (3³⁴ : 3³⁴) / (3³⁷: 3³⁴) = 3⁽³⁴⁻³⁴⁾/3⁽³⁷⁻³⁴⁾ = 3⁰/3³ = 1/27

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27³⁰/3⁹¹ = (3³)³⁰ / 3⁹¹ = 3⁽³ˣ³⁰⁾/3⁹¹ = 3⁹⁰/3⁹¹ = 1/3

- se simplifică cu 3⁹⁰:  (3⁹⁰: 3⁹⁰)/(3⁹¹: 3⁹⁰) = 3⁽⁹⁰⁻⁹⁰⁾ /(3⁹¹⁻⁹⁰⁾ = 3⁰/3¹=1/3

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81¹⁹/9³⁹ = (3⁴)¹⁹ / (3²)³⁹ = 3⁽⁴ˣ¹⁹⁾/3⁽²ˣ³⁹⁾ = 3⁷⁶/3⁷⁸ = 1/3²= 1/9

- se simplifică cu 3⁷⁶

   (3⁷⁶: 3⁷⁶) /(3⁷⁸: 3⁷⁶) = 3⁽⁷⁶⁻⁷⁶⁾/3⁽⁷⁸⁻⁷⁶⁾ = 3⁰/3² = 1/9