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
Explicație pas cu pas:
[tex] \bf a = \big(16^{10} \big)^{100}: \big(4^{20} \big)^{50} \cdot2[/tex]
[tex] \bf a = 16^{10 \cdot100}: 4^{20 \cdot50} \cdot2[/tex]
[tex] \bf a = 16^{1000}: 4^{1000} \cdot2[/tex]
[tex]\bf a = \big(2^{4} \big)^{1000}: \big(2^{2} \big)^{1000} \cdot2[/tex]
[tex]\bf a = 2^{4\cdot1000}: 2^{2 \cdot1000} \cdot2[/tex]
[tex]\bf a = 2^{4000}: 2^{2000} \cdot2^{1} [/tex]
[tex]\bf a = 2^{4000 -2000 +1} [/tex]
[tex]\bf a = 2^{2001} [/tex]
[tex]\bf a = 2^{667 \cdot3} [/tex]
[tex] \red{ \boxed{\bf a = \big( 2^{667} \big)^{3} \: \implies \: cub \: perfect}}[/tex]
