Question

Qual o valor da expressão 2^-3+2×2^-2-2^-4

Answer 1

$2^{-3}~+~2\times2^{-2}~-~2^{-4}~=\\\\\\Utilizando~as~propriedades\\\\\rightarrow~(a)^{-b}~=~\left(\frac{1}{a}\right)^b\\\\\rightarrow~(a)^b\times(a)^c~=~(a)^{b+c}\\\\\\\\=~\left(\frac{1}{2}\right)^3~+~2^{-2+1}~-~\left(\frac{1}{2}\right)^4\\\\\\=~\frac{1^3}{2^3}~+~2^{-1}~-~\frac{1^4}{2^4}\\\\\\=~\frac{1^3}{2^3}~+~2^{-1}~-~\frac{1^4}{2^4}\\\\\\=~\frac{1}{8}~+~\frac{1}{2}~-~\frac{1}{16}\\\\\\MMC~=~16\\\\\\=~\frac{2\,.\,1~+~8\,.\,1~-~1\,.\,1}{16}$

$=~\frac{2~+~8~-~1}{16}\\\\\\=~\boxed{\frac{9}{16}}$

Answer 2

Resposta:

9/16

Explicação passo-a-passo:

= 2^-3+2×2^-2-2^-4

= (1/2)^3 + 2^(1-2) - (1/2)^4

= 1/8 + 2^(-1) - 1/16

= 1/8 + 1/2 - 1/16

Mmc (8,2,16)= 16

= (2.1 + 8.1 - 1)/16

= (2+8-1)/16

= 9/16