Question

(2¹⁰-2⁹)x(2⁹-2⁸)x(2⁸-2⁷):2²⁴ toată desfasurarea​

Answer 1

Răspuns: 1

Explicație pas cu pas:

$(2^{10}-2^{9})\cdot (2^{9}-2^{8})\cdot(2^{8}-2^{7}):2^{24} =$

$2^{9}\cdot(2^{10-9}-2^{9-9})\cdot 2^{8}\cdot(2^{9-8}-2^{8-8})\cdot2^{7}\cdot(2^{8-7}-2^{7-7}):2^{24} =$

$2^{9}\cdot(2^{1}-2^{0})\cdot 2^{8}\cdot(2^{1}-2^{0})\cdot2^{7}\cdot(2^{1}-2^{0}):2^{24} =$

$2^{9}\cdot(2-1)\cdot 2^{8}\cdot(2-1)\cdot2^{7}\cdot(2-1):2^{24} =$

$2^{9}\cdot 1\cdot 2^{8}\cdot 1\cdot2^{7}\cdot 1:2^{24} =$

$2^{9}\cdot 2^{8}\cdot 2^{7}:2^{24} =$

$2^{9+8+7}:2^{24} =$

$2^{24}:2^{24} =2^{24-21}=2^{0} =\boxed{\:1\:}$