Question

Qual o valor de S, sabendo que:

a parte cortada só ta escrito "obtém-se"
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Answer 1

Resposta:

$S = x^{-94}$

Explicação passo a passo:

$S = \frac{(x^{-2})^{16}\cdot[(-x^{-2})^{81}]^{-1}}{x^8\cdot[(-x^3)^9]^8}\\\\S = \frac{x^{-32}\cdot[(-x)^{-162}]^{-1}}{x^8\cdot[(-x)^{27}]^8}\\\\S = \frac{x^{-32}\cdot[-x]^{162}}{x^8\cdot[-x]^{216}}\\\\S = x^{-32}\cdot x^{-8} \cdot[-x]^{162}\cdot [-x]^{-216} \\\\S = x^{-32+(-8)}\cdot [-x]^{162+(-216)}\\\\S = x^{-40}\cdot [-x]^{-54}\\\\S = \frac{1}{x^{40}} \cdot \frac{1}{(-x)^{54}}$

mas como

$(x)^{2n} = (-x)^{2n}$

Então temos que

$S = \frac{1}{x^{40}} \cdot\frac{1}{(x)^{54}}\\\\S = \frac{1}{x^{40+54}} = \frac{1}{x^{94}} = x^{-94}$