Determine o valor de z:
![z= \left[\begin{array}{ccc}(1+ \frac{1}{0,5}) ^{-1} .(1- \frac{1}{0,5}) ^{-1} \\\\\end{array}\right] ^{-2}](https://tex.z-dn.net/?f=+z%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%281%2B+%5Cfrac%7B1%7D%7B0%2C5%7D%29+%5E%7B-1%7D+.%281-+%5Cfrac%7B1%7D%7B0%2C5%7D%29+%5E%7B-1%7D++%5C%5C%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5E%7B-2%7D++ "z= \left[\begin{array}{ccc}(1+ \frac{1}{0,5}) ^{-1} .(1- \frac{1}{0,5}) ^{-1} \\\\\end{array}\right] ^{-2}")
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Olá Mari!
![\\ \mathsf{z = \left [ \left ( 1 + \frac{1}{0,5} \right )^{- 1} \cdot \left ( 1 - \frac{1}{0,5} \right )^{- 1} \right ]^{- 2}} \\\\\\ \mathsf{z = \left [ \left ( 1 + \frac{1}{\frac{1}{2}} \right )^{- 1} \cdot \left ( 1 - \frac{1}{\frac{1}{2}} \right )^{- 1} \right ]^{- 2}} \\\\\\ \mathsf{z = \left [ \left ( 1 + 1 \cdot \frac{2}{1} \right )^{- 1} \cdot \left ( 1 - 1 \cdot \frac{2}{1} \right )^{- 1} \right ]^{- 2}} \\\\\\ \mathsf{z = \left [ \left ( 3 \right )^{- 1} \cdot \left ( - 1 \right )^{- 1} \right ]^{- 2}}](https://tex.z-dn.net/?f=%5C%5C+%5Cmathsf%7Bz+%3D+%5Cleft+%5B+%5Cleft+%28+1+%2B+%5Cfrac%7B1%7D%7B0%2C5%7D+%5Cright+%29%5E%7B-+1%7D+%5Ccdot+%5Cleft+%28+1+-+%5Cfrac%7B1%7D%7B0%2C5%7D+%5Cright+%29%5E%7B-+1%7D+%5Cright+%5D%5E%7B-+2%7D%7D+%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bz+%3D+%5Cleft+%5B+%5Cleft+%28+1+%2B+%5Cfrac%7B1%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D+%5Cright+%29%5E%7B-+1%7D+%5Ccdot+%5Cleft+%28+1+-+%5Cfrac%7B1%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D+%5Cright+%29%5E%7B-+1%7D+%5Cright+%5D%5E%7B-+2%7D%7D+%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bz+%3D+%5Cleft+%5B+%5Cleft+%28+1+%2B+1+%5Ccdot+%5Cfrac%7B2%7D%7B1%7D+%5Cright+%29%5E%7B-+1%7D+%5Ccdot+%5Cleft+%28+1+-+1+%5Ccdot+%5Cfrac%7B2%7D%7B1%7D+%5Cright+%29%5E%7B-+1%7D+%5Cright+%5D%5E%7B-+2%7D%7D+%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bz+%3D+%5Cleft+%5B+%5Cleft+%28+3+%5Cright+%29%5E%7B-+1%7D+%5Ccdot+%5Cleft+%28+-+1+%5Cright+%29%5E%7B-+1%7D+%5Cright+%5D%5E%7B-+2%7D%7D "\\ \mathsf{z = \left [ \left ( 1 + \frac{1}{0,5} \right )^{- 1} \cdot \left ( 1 - \frac{1}{0,5} \right )^{- 1} \right ]^{- 2}} \\\\\\ \mathsf{z = \left [ \left ( 1 + \frac{1}{\frac{1}{2}} \right )^{- 1} \cdot \left ( 1 - \frac{1}{\frac{1}{2}} \right )^{- 1} \right ]^{- 2}} \\\\\\ \mathsf{z = \left [ \left ( 1 + 1 \cdot \frac{2}{1} \right )^{- 1} \cdot \left ( 1 - 1 \cdot \frac{2}{1} \right )^{- 1} \right ]^{- 2}} \\\\\\ \mathsf{z = \left [ \left ( 3 \right )^{- 1} \cdot \left ( - 1 \right )^{- 1} \right ]^{- 2}}")
![\\ \mathsf{z = \left [ \left ( \frac{1}{3} \right )^{+ 1} \cdot \left ( \frac{1}{- 1} \right )^{+ 1} \right ]^{- 2}} \\\\\\ \mathsf{z = \left [ \frac{1}{3} \cdot (- 1) \right ]^{- 2}} \\\\\\ \mathsf{z = \left ( - \frac{1}{3} \right )^{- 2}} \\\\\\ \mathsf{z = \left ( - \frac{3}{1} \right )^{+ 2}} \\\\\\ \boxed{\mathsf{z = 9}}](https://tex.z-dn.net/?f=%5C%5C+%5Cmathsf%7Bz+%3D+%5Cleft+%5B+%5Cleft+%28+%5Cfrac%7B1%7D%7B3%7D+%5Cright+%29%5E%7B%2B+1%7D+%5Ccdot+%5Cleft+%28+%5Cfrac%7B1%7D%7B-+1%7D+%5Cright+%29%5E%7B%2B+1%7D+%5Cright+%5D%5E%7B-+2%7D%7D+%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bz+%3D+%5Cleft+%5B+%5Cfrac%7B1%7D%7B3%7D+%5Ccdot+%28-+1%29+%5Cright+%5D%5E%7B-+2%7D%7D+%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bz+%3D+%5Cleft+%28+-+%5Cfrac%7B1%7D%7B3%7D+%5Cright+%29%5E%7B-+2%7D%7D+%5C%5C%5C%5C%5C%5C+%5Cmathsf%7Bz+%3D+%5Cleft+%28+-+%5Cfrac%7B3%7D%7B1%7D+%5Cright+%29%5E%7B%2B+2%7D%7D+%5C%5C%5C%5C%5C%5C+%5Cboxed%7B%5Cmathsf%7Bz+%3D+9%7D%7D "\\ \mathsf{z = \left [ \left ( \frac{1}{3} \right )^{+ 1} \cdot \left ( \frac{1}{- 1} \right )^{+ 1} \right ]^{- 2}} \\\\\\ \mathsf{z = \left [ \frac{1}{3} \cdot (- 1) \right ]^{- 2}} \\\\\\ \mathsf{z = \left ( - \frac{1}{3} \right )^{- 2}} \\\\\\ \mathsf{z = \left ( - \frac{3}{1} \right )^{+ 2}} \\\\\\ \boxed{\mathsf{z = 9}}")
MariKetlin:
Muito obrigada
Não há de quê!
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