Question

reduzir essas potências​

Answer 1

Resposta:

Solução:

c)

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \big[(0,05)^3 \big]^{-\:2} \cdot \left ( \dfrac{5}{100} \right )^5 = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \Bigg[ \left ( \dfrac{5}{100} \right )^3 \bigg]^{-\:2} \cdot \left ( \dfrac{5}{100} \right )^5 = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{5}{100} \right )^{-6} \cdot \left ( \dfrac{5}{100} \right )^5 = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{5}{100} \right )^{-6 +5} = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{5}{100} \right )^{-1} = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{100}{5} \right )^{1} = \left ( \dfrac{100}{5} \right ) = 20 \end{array}\right$

Logo:

$\boxed{ \boxed { \boldsymbol{\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \big[(0,05)^3 \big]^{-\:2} \cdot \left ( \dfrac{5}{100} \right )^5 = 20\end{array}\right }}} \quad \gets \mathbf{ Resposta }$

d)

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{3}{2} \right )^{-2} \div \left ( \dfrac{2}{3} \right )^3 = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{2}{3} \right )^{2} \div \left ( \dfrac{2}{3} \right )^3 = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{4}{9} \right ) \div \left ( \dfrac{8}{27} \right ) = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{4 \div 4}{9 \div 9} \right ) \cdot \left ( \dfrac{27 \div 9}{8 \div 4} \right ) = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{1}{1} \right ) \cdot \left ( \dfrac{3}{2} \right ) = \dfrac{3}{2} \end{array}\right$

Logo:

$\boxed{ \boxed { \boldsymbol{\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{3}{2} \right )^{-2} \div \left ( \dfrac{2}{3} \right )^2 = \dfrac{3}{2} \end{array}\right }}} \quad \gets \mathbf{ Resposta }$

e)

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( 3,2 \right )^2 \cdot 6^{-1} \cdot \left ( \dfrac{1}{6} \right )^{-4} = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left \left ( \dfrac{32}{10} \right )^2 \cdot 6^{-1} \cdot 6^{4} = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left \left ( \dfrac{32}{10} \right )^2 \cdot 6^{-1 +4} = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left \left ( \dfrac{32}{10} \right )^2 \cdot 6^{3} = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \dfrac{1024}{100} \cdot 216 = \dfrac{221184}{100} = 2211,84 \end{array}\right$

Logo:

$\boxed{ \boxed { \boldsymbol{ \large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( 3,2 \right )^2 \cdot 6^{-1} \cdot \left ( \dfrac{1}{6} \right )^{-4} = 2\:211,84 \end{array}\right }}} \quad \gets \mathbf{ Resposta }$

f)

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \Bigg\{\Bigg[ \left ( \dfrac{5}{7} \right )^ {-2} \Bigg]^{\frac{1}{2}} \Bigg\}^3 = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \Bigg\{ \left ( \dfrac{5}{7} \right )^ {-2 \cdot \frac{1}{2} } \Bigg\}^3 = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \Bigg\{ \left ( \dfrac{5}{7} \right )^ {-\: \frac{2}{2} } \Bigg\}^3 = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \Bigg\{ \left ( \dfrac{5}{7} \right )^ {-\: 1 } \Bigg\}^3 = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{5}{7} \right )^ {-\: 1 \times 3 } = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{5}{7} \right )^ {-\: 3 } = \end{array}\right$

$\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \left ( \dfrac{7}{5} \right )^ { 3 } = \dfrac{343}{125} \end{array}\right$

Logo:

$\boxed{ \boxed { \boldsymbol{\large \sf \displaystyle \left\begin{array}{l l l l l } \sf \Bigg\{\Bigg[ \left ( \dfrac{5}{7} \right )^ {-2} \Bigg]^{\frac{1}{2}} \Bigg\}^3 = \end{array}\right \dfrac{343}{125} }}} \quad \gets \mathbf{ Resposta }$

Explicação passo-a-passo:

RESOLVENDO EXPRESSÕES NUMÉRICAS:

Ordem das operações:

Potenciação e Radiciação

Multiplicação e Divisão

Soma e Subtração

Usando símbolos:

as operações que estão dentro dos parênteses

as operações que estão dentro dos colchetes

as operações que estão dentro das chaves

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https://brainly.com.br/tarefa/39601632