Question

como resolver 100^5 . 1000^7 . (100^2)^-4 .10000^-3

Answer 1

E aí Sidney,

use a propriedade da exponenciação:

$a^m\cdot a^n~\to~a^{m+n}\\\\ (a^m)^n~\to~a^{m\cdot n}$

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$100^5\cdot1.000^7\cdot(100^2)^{-4}\cdot10.000^{-3}=100^5\cdot100^8\cdot100^{-8}\cdot100^{-5}~~.\\\\ 100^5\cdot1.000^7\cdot(100^2)^{-4}\cdot10.000^{-3}=100^{5+8-8-5}\\\\ 100^5\cdot1.000^7\cdot(100^2)^{-4}\cdot10.000^{-3}=100^0\\\\ \large\boxed{\boxed{100^5\cdot1.000^7\cdot(100^2)^{-4}\cdot10.000^{-3}=1}}.\\.$

Tenha ótimos estudos =))

Answer 2

Nós podemos escrever também dessa maneira:
$100^{5} *1000^{7}*100^{-8}*10000^{-3} = \\100^{5-8}*1000^{7}*(10000/1)^{-3} =\\ 100^{-3}*1000^{7}*(1/10000)^{3} = \\1/100^{3}*1000^{7}*(1/10000)^{3} = \\ 1000^{7}/100^{3}*10000^{3} = \\ 1000^{7}/100^3*(100^2)^{3}= \\ 1000^7/100^3*100^6= \\ 1000^7/100^{3+6} = \\ 1000^7/100^9 = \\ (10^3)^7/(10^2)^9 = \\ 10^{21}/10^{18} = 10^{21-18} = 10^{4} = 10000$