Question

E10. Fie numărul natural a = (16¹⁰)¹⁰⁰:(4²⁰)⁵⁰×2 Determinați dacă a este cub perfect. Justificati pun puncte si dau coroana dar am nevoie de raspuns repede​

Answer 1

Răspuns:

a = (16¹⁰)¹⁰⁰:(4²⁰)⁵⁰×2

a=(2⁴)¹⁰⁰⁰:(2²)¹⁰⁰⁰·2

a=2⁴⁰⁰⁰:2²⁰⁰⁰·2

a=2²⁰⁰⁰·2

a=2²⁰⁰⁰⁺¹=2²⁰⁰¹

a=(2⁶⁶⁷)³ este un cub perfect

Answer 2

Explicație pas cu pas:

$\bf a = \big(16^{10} \big)^{100}: \big(4^{20} \big)^{50} \cdot2$

$\bf a = 16^{10 \cdot100}: 4^{20 \cdot50} \cdot2$

$\bf a = 16^{1000}: 4^{1000} \cdot2$

$\bf a = \big(2^{4} \big)^{1000}: \big(2^{2} \big)^{1000} \cdot2$

$\bf a = 2^{4\cdot1000}: 2^{2 \cdot1000} \cdot2$

$\bf a = 2^{4000}: 2^{2000} \cdot2^{1}$

$\bf a = 2^{4000 -2000 +1}$

$\bf a = 2^{2001}$

$\bf a = 2^{667 \cdot3}$

$\red{ \boxed{\bf a = \big( 2^{667} \big)^{3} \: \implies \: cub \: perfect}}$