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simplificar ((x^3y^{-3}z^5)/(x^5y^0z^2))^{-1}

Solução

simplificar

(\frac{x ^{3} y ^{- 3} z ^{5}}{x ^{5} y ^{0} z ^{2}})^{- 1}

\frac{x ^{2} y ^{3}}{z ^{3}}

Passos da solução

(\frac{x ^{3} y ^{- 3} z ^{5}}{x ^{5} y ^{0} z ^{2}})^{- 1}

Aplicar as propriedades dos expoentes:

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

(\frac{x ^{3} y ^{- 3} z ^{5}}{x ^{5} y ^{0} z ^{2}})^{- 1} = \frac{1}{\frac{x ^{3} y ^{- 3} z ^{5}}{x ^{5} y ^{0} z ^{2}}}

= \frac{1}{\frac{x ^{3} y ^{- 3} z ^{5}}{x ^{5} y ^{0} z ^{2}}}

Aplicar a regra

a^{0} = 1, a \neq = 0

y^{0} = 1

= \frac{1}{\frac{x ^{3} y ^{- 3} z ^{5}}{1 \cdot x ^{5} z ^{2}}}

Multiplicar:

1 \cdot z^{2} = z^{2}

= \frac{1}{\frac{x ^{3} y ^{- 3} z ^{5}}{x ^{5} z ^{2}}}

Aplicar as propriedades das frações:

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

= \frac{x ^{5} z ^{2}}{x ^{3} y ^{- 3} z ^{5}}

Aplicar as propriedades dos expoentes:

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

\frac{x ^{5}}{x ^{3}} = x^{5 - 3}

= \frac{z ^{2} x ^{5 - 3}}{y ^{- 3} z ^{5}}

Subtrair:

5 - 3 = 2

= \frac{x ^{2} z ^{2}}{y ^{- 3} z ^{5}}

Aplicar as propriedades dos expoentes:

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

\frac{z ^{2}}{z ^{5}} = \frac{1}{z ^{5 - 2}}

= \frac{x ^{2}}{y ^{- 3} z ^{5 - 2}}

Subtrair:

5 - 2 = 3

= \frac{x ^{2}}{y ^{- 3} z ^{3}}

y^{- 3} = \frac{1}{y ^{3}}

= \frac{x ^{2}}{\frac{1}{y ^{3}} z ^{3}}

Multiplicar

\frac{1}{y ^{3}} z^{3} : \frac{z ^{3}}{y ^{3}}

= \frac{x ^{2}}{\frac{z ^{3}}{y ^{3}}}

Aplicar as propriedades das frações:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{x ^{2} y ^{3}}{z ^{3}}

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