Question

Calculati: 12^120x16^30:9^60:8^40​

Answer 1

Răspuns:

12¹²⁰x16³⁰:9⁶⁰:8⁴⁰=2²⁴⁰

Explicație pas cu pas:

Calculati: 12^120x16^30:9^60:8^40​

12¹²⁰x16³⁰:9⁶⁰:8⁴⁰= (2²x3)¹²⁰x(2⁴)³⁰:(3²)⁶⁰:(2³)⁴⁰=(2²)¹²⁰x3¹²⁰x2⁽⁴ˣ³⁰⁾:3⁽²ˣ⁶⁰⁾:2⁽³ˣ⁴⁰⁾= 2⁽²ˣ¹²⁰⁾x3¹²⁰x2¹²⁰:3¹²⁰:2¹²⁰ =

2²⁴⁰x2¹²⁰x3¹²⁰:3¹²⁰:2¹²⁰=2⁽²⁴⁰⁺¹²⁰⁾x3¹²⁰:3¹²⁰:2¹²⁰= 2³⁶⁰x3⁽¹²⁰⁻¹²⁰⁾:2¹²⁰= 2³⁶⁰x3⁰:2¹²⁰= 2³⁶⁰:2¹²⁰=2⁽³⁶⁰⁻¹²⁰⁾=2²⁴⁰    

Answer 2

$\it 12^{120}\cdot16^{30}:9^{60}:8^{40}= 12^{120}\cdot16^{30}:(9^{60}\cdot8^{40})\\ \\ 12^{120}\cdot16^{30}=12^{120}\cdot(2^4)^{30}=12^{120}\cdot2^{120}=24^{120}\\ \\ 9^{60}\cdot8^{40}=(3^2)^{60}\cdot(2^3)^{40}=3^{120}\cdot2^{120}=6^{120}$

Acum, exercițiul devine:

$\it 24^{120}:6^{120}=(24:6)^{120}=4^{120}$