Respostas

2014-08-17T22:11:32-03:00
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 =))
1 5 1
2014-08-17T22:28:42-03:00
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