simplificar sqrt(((27)/(y^3))^{-2/3)}

Solução

simplificar

(\frac{27}{y ^{3}})^{- \frac{2}{3}}

\frac{y}{3}

Passos da solução

(\frac{27}{y ^{3}})^{- \frac{2}{3}}

Aplicar a seguinte propriedade dos radicais:

n a^{m} = a^{\frac{m}{n}},

assumindo que

a \geq 0

(\frac{27}{y ^{3}})^{- \frac{2}{3}} = (\frac{27}{y ^{3}})^{\frac{- \frac{2}{3}}{2}}

= (\frac{27}{y ^{3}})^{\frac{- \frac{2}{3}}{2}}

\frac{- \frac{2}{3}}{2} = - \frac{1}{3}

= (\frac{27}{y ^{3}})^{- \frac{1}{3}}

Aplicar as propriedades dos expoentes:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{( \frac{27}{y ^{3}} ) ^{\frac{1}{3}}}

Aplicar a seguinte propriedade dos radicais:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}},

assumindo que

a \geq 0, b \geq 0

(\frac{27}{y ^{3}})^{\frac{1}{3}} = \frac{2 7 ^{\frac{1}{3}}}{( y ^{3} ) ^{\frac{1}{3}}}

= \frac{1}{\frac{2 7 ^{\frac{1}{3}}}{( y ^{3} ) ^{\frac{1}{3}}}}

2 7^{\frac{1}{3}} = 3

= \frac{1}{\frac{3}{( y ^{3} ) ^{\frac{1}{3}}}}

Aplicar as propriedades das frações:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{( y ^{3} ) ^{\frac{1}{3}}}{3}

Simplificar

(y^{3})^{\frac{1}{3}} : y

= \frac{y}{3}

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