Question

3) Determine o valor das expressões:

Answer 1

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$\large\boxed{\begin{array}{l}\rm a)~\sf 2^{-1}+6\cdot\bigg(\dfrac{2}{3}\bigg)^{-2}-\bigg(-\dfrac{1}{3}\bigg)^{-1}\\\sf=\bigg(\dfrac{1}{2}\bigg)^1+6\cdot\bigg(\dfrac{3}{2}\bigg)^2-(-3)^1\\\sf=\dfrac{1}{2}+\diagup\!\!\!6^3\cdot\dfrac{9}{\diagup\!\!\!4_2}-(-3)\\\sf=\dfrac{1}{2}+\dfrac{27}{2}+3=\dfrac{1+27+6}{2}\\\sf=\dfrac{34}{2}=17\end{array}}\blue{\checkmark}$

$\boxed{\begin{array}{l}\rm b)~\sf\bigg(\dfrac{1}{2}\bigg)^{-4}\div\dfrac{1}{2}\cdot(4^{-1})^2+\bigg(-\dfrac{1}{6}\bigg)^0\\\sf 2^4\div\dfrac{1}{2}\cdot\bigg(\dfrac{1}{4}\bigg)^2+1\\\sf16\div\dfrac{1}{2}\cdot\dfrac{1}{16}+1\\\sf \diagdown\!\!\!\!\!\!16\cdot2\cdot\dfrac{1}{\diagdown\!\!\!\!\!16}+1=2+1=3\end{array}}\blue{\checkmark}$