Question

calcule o valor da expressão:
2/3 elevado a -2 - 1/2 elevado a -1 + 1/4 elevado a -2​

Answer 1

Resposta:

$\sf A = \left(\dfrac{2}{3} \right)^{-\,2} - \left(\dfrac{1}{2} \right)^{-\,1} + \left(-\;\dfrac{1}{4} \right)^{-\,2} \quad \gets \mbox{\sf inverter as fra{\c c}{\~o}es, expoente positivo.}$

$\sf A = \left(\dfrac{3}{2} \right)^{2} - \left(\dfrac{2}{1} \right)^{1} + \left(-\;\dfrac{4}{1} \right)^{2}$

$\sf A = \dfrac{9}{4} - \dfrac{4}{1}+ \left(+\dfrac{16}{1} \right)$

$\sf A = \dfrac{9}{4} - \dfrac{4}{1} + \dfrac{16}{1 }$

$\sf A = \dfrac{9}{4} + \dfrac{12}{1 } \quad \gets \text{ \sf m.m.c de ( 4 e 1) = 4}.}$

$\sf A = \dfrac{9}{4} + \dfrac{48}{4 }$

$\boxed{ \boxed { \boldsymbol{ \sf \displaystyle A = \dfrac{57}{4} }}} \quad \gets \mathbf{ Resposta }$

Explicação passo-a-passo: