Question

A forma mais simples de escrever a expressão
$2 ^{x} \div 4 ^{x - 5} \times 8 ^{x - 2}$
é:

a)
$2 ^{2x - 16}$
b)
${2}^{3x - 7}$
c)
${2}^{6x - 4}$
d)
${2}^{2x + 4}$
e) N.d.a

Com conta pvr!
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Answer 1

$\large\boxed{\begin{array}{l}\rm A~forma~mais~simples~de~escrever\\\rm a~express\tilde ao~\dfrac{2^x}{4^{x-5}}\cdot 8^{x-2}~\acute e:\\\tt a)~\sf2^{2x-16}\\\tt b)~\sf 2^{3x-7}\\\tt c)~\sf 2^{6x-4}\\\tt d)~\sf 2^{2x+4}\\\tt e)~\sf N.D.A\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao}\\\sf\dfrac{2^x}{4^{x-5}}\cdot8^{x-2}=\dfrac{2^x}{(2^2)^{x-5}}\cdot(2^3)^{x-2}\\\sf=\dfrac{2^x}{2^{2x-10}}\cdot2^{3x-6}=\dfrac{2^{x+3x-6}}{2^{2x-10}}\\\sf =\dfrac{2^{4x-6}}{2^{2x-10}}=2^{4x-6-(2x-10)}\\\sf=2^{4x-6-2x+10}=2^{2x+4}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~d}}}}\end{array}}$