Question

(1/2) elevado a 4 ÷ (1/2) elevado a 6, usando as propriedades da potênciação

Answer 1

$\frac{\left(\frac{1}{2}\right)^4}{\left(\frac{1}{2}\right)^6}=4$

$\frac{\left(\frac{1}{2}\right)^4}{\left(\frac{1}{2}\right)^6}$

$\mathrm{Aplicar\:as\:propriedades\:dos\:expoentes}:\quad \frac{x^a}{x^b}=x^{a-b}$

$\frac{\left(\frac{1}{2}\right)^4}{\left(\frac{1}{2}\right)^6}=\left(\frac{1}{2}\right)^{4-6}$

$=\left(\frac{1}{2}\right)^{-2}$

$\mathrm{Aplicar\:as\:propriedades\:dos\:expoentes}:\quad \:a^{-b}=\frac{1}{a^b}$

$\left(\frac{1}{2}\right)^{-2} = \frac{1}{\left(\frac{1}{2}\right)^2}$

$\mathrm{Aplicar\:as\:propriedades\:dos\:expoentes}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$

$\left(\frac{1}{2}\right)^2=\frac{1^2}{2^2}$

$\frac{1}{\left(\frac{1}{2}\right)^2} = \frac{1}{\frac{1^2}{2^2}}$

$\mathrm{Aplicar\:as\:propriedades\:das\:fracoes}:\quad \frac{1}{\frac{b}{c}}=\frac{c}{b}$

$\frac{1}{\frac{1^2}{2^2}} = \frac{2^2}{1^2}$

$\mathrm{Aplicar\:a\:regra}\:1^a=1$

$=\frac{2^2}{1}$

$2^2=4$