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simplificar (((8x^3y^2z))/((12y^3z^2x)))^3

Solução

simplificar

(\frac{( 8 x ^{3} \cdot y ^{2} \cdot z )}{( 12 y ^{3} \cdot z ^{2} \cdot x )})^{3}

\frac{8 x ^{6}}{27 y ^{3} z ^{3}}

Passos da solução

(\frac{8 x ^{3} y ^{2} z}{12 y ^{3} z ^{2} x})^{3}

Aplicar as propriedades dos expoentes:

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

= \frac{( 8 x ^{3} y ^{2} z ) ^{3}}{( 12 y ^{3} z ^{2} x ) ^{3}}

Simplificar

(8 x^{3} y^{2} z)^{3} : 512 x^{9} y^{6} z^{3}

= \frac{512 x ^{9} y ^{6} z ^{3}}{( 12 y ^{3} z ^{2} x ) ^{3}}

Simplificar

(12 y^{3} z^{2} x)^{3} : 1728 y^{9} z^{6} x^{3}

= \frac{512 x ^{9} y ^{6} z ^{3}}{1728 y ^{9} z ^{6} x ^{3}}

Eliminar o fator comum:

64

= \frac{8 x ^{9} y ^{6} z ^{3}}{27 x ^{3} y ^{9} z ^{6}}

Aplicar as propriedades dos expoentes:

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

\frac{x ^{9}}{x ^{3}} = x^{9 - 3}

= \frac{8 y ^{6} z ^{3} x ^{9 - 3}}{27 y ^{9} z ^{6}}

Subtrair:

9 - 3 = 6

= \frac{8 x ^{6} y ^{6} z ^{3}}{27 y ^{9} z ^{6}}

Aplicar as propriedades dos expoentes:

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

\frac{y ^{6}}{y ^{9}} = \frac{1}{y ^{9 - 6}}

= \frac{8 x ^{6} z ^{3}}{27 z ^{6} y ^{9 - 6}}

Subtrair:

9 - 6 = 3

= \frac{8 x ^{6} z ^{3}}{27 y ^{3} z ^{6}}

Aplicar as propriedades dos expoentes:

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

\frac{z ^{3}}{z ^{6}} = \frac{1}{z ^{6 - 3}}

= \frac{8 x ^{6}}{27 y ^{3} z ^{6 - 3}}

Subtrair:

6 - 3 = 3

= \frac{8 x ^{6}}{27 y ^{3} z ^{3}}

f a c t or 5 x^{2} + 33 x y - 14 y^{2}

s im pl i f y (1 + a^{2})^{- 2}

f a c t or - x^{2} - x - 2

s im pl i f y (x^{x})^{2 x}

s im pl i f y (e + r) i^{2}