Question

calcule as potências de expoente negativo​

Answer 1

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⠀⠀☞ As potências são: a) 1/2; b) 1/4; c) 1/4; d) -1/8; e) 2; f) -2; g) 16 ✅

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⚡ " -O que representa um expoente negativo?"

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➡️⠀Que devemos inverter a base, ou seja, tomar o valor inverso da base.

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⚡ " -O que seria o valor inverso de um número?"

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➡️⠀É o valor que quando multiplicado pelo número resultará no elemento neutro da multiplicação: 1. Para isso, basta invertermos numerador e denominador daquele número (na ausência de um denominador consideramos ele igual à 1).

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a) 2⁻¹

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$\LARGE\blue{\sf \left(\dfrac{2}{1}\right)^{-1} = \left(\dfrac{1}{2}\right)^1}$

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$\LARGE\blue{\sf = \dfrac{1^1}{2^1}}$

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$\LARGE\blue{\sf = \dfrac{1}{2}}$  

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$\huge\green{\boxed{\rm~~~\red{a)}~\gray{2^{-1}}~\pink{=}~\blue{ \dfrac{1}{2} }~~~}}$ ✅

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b) 2⁻²

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$\LARGE\blue{\sf \left(\dfrac{2}{1}\right)^{-2} = \left(\dfrac{1}{2}\right)^2}$

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$\LARGE\blue{\sf = \dfrac{1^2}{2^2}}$

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$\LARGE\blue{\sf = \dfrac{1}{4}}$  

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$\huge\green{\boxed{\rm~~~\red{b)}~\gray{2^{-2}}~\pink{=}~\blue{ \dfrac{1}{4} }~~~}}$ ✅

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c) (-2)⁻²

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$\LARGE\blue{\sf \left(\dfrac{-2}{1}\right)^{-2} = \left(\dfrac{-1}{2}\right)^2}$

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$\LARGE\blue{\sf = \dfrac{(-1)^2}{2^2}}$

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$\LARGE\blue{\sf = \dfrac{1}{4}}$  

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$\huge\green{\boxed{\rm~~~\red{c)}~\gray{(-2)^{-2}}~\pink{=}~\blue{ \dfrac{1}{4} }~~~}}$ ✅

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d) (-2)⁻³

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$\LARGE\blue{\sf \left(\dfrac{-2}{1}\right)^{-3} = \left(\dfrac{-1}{2}\right)^3}$

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$\LARGE\blue{\sf = \dfrac{(-1)^3}{2^3}}$

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$\LARGE\blue{\sf = \dfrac{-1}{8}}$  

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$\huge\green{\boxed{\rm~~~\red{d)}~\gray{(-2)^{-3}}~\pink{=}~\blue{ \dfrac{-1}{8} }~~~}}$ ✅

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e) (1/2)⁻¹

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$\LARGE\blue{\sf \left(\dfrac{1}{2}\right)^{-1} = 2^1}$

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$\LARGE\blue{\sf = 2}$  

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$\huge\green{\boxed{\rm~~~\red{e)}~\gray{\left(\dfrac{1}{2}\right)^{-1}}~\pink{=}~\blue{ 2 }~~~}}$ ✅

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f) (-1/2)⁻¹

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$\LARGE\blue{\sf \left(\dfrac{-1}{2}\right)^{-1} = (-2)^1}$

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$\LARGE\blue{\sf = -2}$  

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$\huge\green{\boxed{\rm~~~\red{f)}~\gray{\left(\dfrac{-1}{2}\right)^{-1}}~\pink{=}~\blue{ -2 }~~~}}$ ✅

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g) (-1/2)⁻⁴

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$\LARGE\blue{\sf \left(\dfrac{-1}{2}\right)^{-4} = (-2)^4}$

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$\LARGE\blue{\sf = 16}$  

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$\huge\green{\boxed{\rm~~~\red{g)}~\gray{\left(\dfrac{-1}{2}\right)^{-4}}~\pink{=}~\blue{ 16 }~~~}}$ ✅  

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

⠀⠀☀️ Leia mais sobre potências de base negativa:

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✈ https://brainly.com.br/tarefa/38140981

$\bf\large\red{\underline{\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

⠀⠀⠀⠀☕ $\Large\blue{\text{\bf Bons~estudos.}}$

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($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\purple{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\Huge\green{\text{ \underline{\red{\mathbb{S}}\blue{\mathfrak{oli}}~}~\underline{\red{\mathbb{D}}\blue{\mathfrak{eo}}~}~\underline{\red{\mathbb{G}}\blue{\mathfrak{loria}}~} }}$ ✞

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