Respostas

  • Usuário do Brainly
2014-08-06T15:28:40-03:00
1)
a)

(-3) ^{-2} =( \frac{-1}{3} ) ^{2} = \frac{1}{9}

b)
   ( \frac{7}{8}) ^{-4}  =( \frac{8}{7} ) ^{4} = \frac{4.096}{2.401}

c)
  ( \frac{2}{4} ) ^{-8} =( \frac{1}{2}) ^{-8}  =( \frac{2}{1}) ^{8} =128

Racionalze

d)
 \frac{2}{ \sqrt{3} } = \frac{2. \sqrt{3} }{ \sqrt{3}. \sqrt{3}  } = \frac{2 \sqrt{3} }{3}

e)
   \frac{ \sqrt{3} }{ \sqrt{2} } = \frac{ \sqrt{3}. \sqrt{2}  }{ \sqrt{2}. \sqrt{2}  }= \frac{ \sqrt{6} }2}

f)
    \frac{3}{2 \sqrt{3} } = \frac{3 \sqrt{3} }{2 \sqrt{3}. \sqrt{3}  } = \frac{3 \sqrt{3} }{6} = \frac{ \sqrt{3} }{2}

Calcule

g)
   \sqrt{8} + \sqrt{32} + \sqrt{72} - \sqrt{50} =

 \sqrt{ 2^{2}.2 } + \sqrt{ 2^{4}.2 } + \sqrt{ 2^{2}.2. 3^{2}  } - \sqrt{2. 5^{2} } =

2 \sqrt{2}+4 \sqrt{2} +6 \sqrt{2}  -5 \sqrt{2} =

12 \sqrt{2} -5 \sqrt{2} =7 \sqrt{2}

h)
   \sqrt{32 x^{3} } = \sqrt{ 2^{4} .2. x^{2} .x} =4x \sqrt{2x}

i)
8 ^{ \frac{4}{3} } = \sqrt[3]{ 8^{4} } = \sqrt[3]{( 2^{3}) ^{4}  } = \sqrt[3]{ 2^{12} } = 2^{4} =16
1 5 1
2014-08-06T17:33:33-03:00
Racionalizando, simplificando e calculando as expressões abaixo, temos:
a)  (-3)^{-2} =  \frac{1}{ (-3)^{2} } =  \frac{1}{9}
b)  ( \frac{7}{8}) ^{-4} =  \frac{1}{( \frac{7}{8}) ^{4}}= \frac{1}{ \frac{2401}{4096} }= frac{4096}{2401}   

c)  ( \frac{2}{4})^{-8} =  \frac{1}{( \frac{1}{2}) ^{8} }=  \frac{1}{ \frac{1}{256} }    =256
d)   \frac{2}{ \sqrt{3}}= \frac{2}{ \sqrt{3} }. \frac{ \sqrt{3}}{ \sqrt{3}}= \frac{2 \sqrt{3} }{3}
e)   \frac{ \sqrt{3} }{ \sqrt{2} }=  \frac{ \sqrt{3}}{ \sqrt{2} }. \frac{ \sqrt{2} }{ \sqrt{2}  }= \frac{ \sqrt{6} }{2}

f)   \frac{3}{2 \sqrt{3} }= \frac{3}{2 \sqrt{3} }. \frac{ \sqrt{3} }{ \sqrt{3} }= \frac{3 \sqrt{3} }{6}= \frac{ \sqrt{3} }{2}
g)  \sqrt{8}+ \sqrt{32}+ \sqrt{72} - \sqrt{50}=2 \sqrt{2}+4 \sqrt{2}+6 \sqrt{2}- 5 \sqrt{2}=
7 \sqrt{2}
h)  \sqrt{32 x^{3} }=  \sqrt{ 4^{2} 2 x^{2}x }=4 \sqrt{2}x \sqrt{x}=4x \sqrt{2x}
i)   8^{ \frac{4}{3} }=  \sqrt[3]{ 8^{4} }= \sqrt[3]{( 2^{3}) ^{4} }= \sqrt[3]{( 2^{4}) ^{3}  } = 2^{4}=16
j)  ( \frac{2}{4}) ^{ \frac{-5}{2} }=( \frac{1}{2}) ^{ \frac{-5}{2} }= \sqrt{( \frac{1}{2})  ^{-5} }=
 \sqrt{ \frac{1}{( \frac{1}{2}) ^{5}  } }= \sqrt{ 2^{5} }= \sqrt{ 2^{2}  2^{2} 2}=2.2. \sqrt{2}= 4 \sqrt{2}