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simplificar (2x^2y^{-5})(6x^{-3}y)(1/3 x^{-1}y^3)

Solução

simplificar

(2 x^{2} y^{- 5}) (6 x^{- 3} y) (\frac{1}{3} x^{- 1} y^{3})

\frac{4}{y x ^{2}}

Passos da solução

(2 x^{2} y^{- 5}) (6 x^{- 3} y) (\frac{1}{3} x^{- 1} y^{3})

Simplificar

2 x^{2} y^{- 5} : \frac{2 x ^{2}}{y ^{5}}

= \frac{2 x ^{2}}{y ^{5}} \cdot 6 x^{- 3} y \frac{1}{3} x^{- 1} y^{3}

Aplicar as propriedades dos expoentes:

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

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

= \frac{2 x ^{2}}{y ^{5}} \cdot 6 \cdot \frac{1}{x ^{3}} y \frac{1}{3} x^{- 1} y^{3}

Aplicar as propriedades dos expoentes:

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

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

= \frac{2 x ^{2}}{y ^{5}} \cdot 6 \cdot \frac{1}{x ^{3}} y \frac{1}{3} \cdot \frac{1}{x} y^{3}

Simplificar

y y^{3} : y^{4}

= \frac{2 x ^{2}}{y ^{5}} \cdot 6 \cdot \frac{1}{x ^{3}} y^{4} \frac{1}{3} \cdot \frac{1}{x}

= \frac{1}{3} \cdot 6 y^{4} \frac{2 x ^{2}}{y ^{5}} \cdot \frac{1}{x ^{3}} \cdot \frac{1}{x}

Aplicar as propriedades das frações:

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

= \frac{1 \cdot 6 y ^{4} \cdot 2 x ^{2} \cdot 1 \cdot 1}{3 y ^{5} x ^{3} x}

Simplificar

x^{3} x : x^{4}

= \frac{1 \cdot 6 y ^{4} \cdot 2 x ^{2} \cdot 1 \cdot 1}{3 y ^{5} x ^{4}}

Multiplicar os números:

1 \cdot 6 \cdot 2 \cdot 1 \cdot 1 = 12

= \frac{12 y ^{4} x ^{2}}{3 y ^{5} x ^{4}}

Fatorar o número:

12 = 3 \cdot 4

= \frac{3 \cdot 4 y ^{4} x ^{2}}{3 y ^{5} x ^{4}}

Eliminar o fator comum:

3

= \frac{4 y ^{4} x ^{2}}{y ^{5} x ^{4}}

Simplificar

\frac{y ^{4}}{y ^{5}} : \frac{1}{y}

= \frac{4 x ^{2}}{y x ^{4}}

Simplificar

\frac{x ^{2}}{x ^{4}} : \frac{1}{x ^{2}}

= \frac{4}{y x ^{2}}

- 6 = \frac{n}{2} - 10

- x - 5 + 4 x = - 7 x + 6 x + 15

s im pl i f y 1^{2}

f a c t or 40 a^{2} + 124 a + 60

\frac{k - 10}{2} = - 7