Me ajudem pfvr!! Simplifique:
Soluções para a tarefa
Resposta:
121/36
Explicação passo-a-passo:
(2^98+4^50-8^34)
-------------------------------
(2^99 - 32^20+2^101)
x
(2^98 + 4^50- 8^34)
--------------------------------
(2^99 - 32^20 + 2^101)
Em partes
Parte de cima:
= (2^98+4^50-8^34)
= 2^98 + (2^2)^50 - (2^3)^34
= 2^98 + 2^100 - 2^102
= 2^98.(1+ 2^2 - 2^4)
= 2^98.(1+4-16)
= 2^98.(- 11)
= - 11. 2^98
------------------------------
Parte de baixo:
=(2^99 - 32^20+2^101)
= 2^99 - (2^5)^20 + 2^101
= 2^99 - 2^100 + 2^101
= 2^99(1 - 2^1 + 2^2)
= 2^99.(1 - 2+ 4)
= 2^99.(3)
= 3.2^99
As outras duas:
De cima, igual ao (a)
= - 11. 2^98
De baixo, iguaç ao (b)
= 3.2^99
(- 11).2^98 / 3. 2^99 . (-11).2^98/3.2^99
= (-11).(-11).2^98.2^98/3.3.2^99.2^99
= 121 . 2^196
----------------------
9 . 2^198
= 121 / 9 . 2^198 . 2^(-196)
= 121/9 . 2^2
= 121/9.4
= 121/36