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simplificar ((2d^4)/(4e))^3((4d^2)/(8e))^{-2}

Solución

simplificar

(\frac{2 d ^{4}}{4 e})^{3} (\frac{4 d ^{2}}{8 e})^{- 2}

\frac{d ^{8}}{2 e}

Pasos de solución

(\frac{2 d ^{4}}{4 e})^{3} (\frac{4 d ^{2}}{8 e})^{- 2}

Aplicar las leyes de los exponentes:

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

= (\frac{2 d ^{4}}{4 e})^{3} \frac{1}{( \frac{4 d ^{2}}{8 e} ) ^{2}}

(\frac{2 d ^{4}}{4 e})^{3} = \frac{d ^{12}}{2 ^{3} e ^{3}}

= \frac{1}{( \frac{4 d ^{2}}{8 e} ) ^{2}} \cdot \frac{d ^{12}}{2 ^{3} e ^{3}}

\frac{1}{( \frac{4 d ^{2}}{8 e} ) ^{2}} = \frac{2 ^{2} e ^{2}}{d ^{4}}

= \frac{2 ^{2} e ^{2}}{d ^{4}} \cdot \frac{d ^{12}}{2 ^{3} e ^{3}}

Multiplicar fracciones:

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

= \frac{d ^{12} \cdot 2 ^{2} e ^{2}}{2 ^{3} e ^{3} d ^{4}}

Aplicar las leyes de los exponentes:

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

\frac{d ^{12}}{d ^{4}} = d^{12 - 4}

= \frac{2 ^{2} e ^{2} d ^{12 - 4}}{2 ^{3} e ^{3}}

Restar:

12 - 4 = 8

= \frac{2 ^{2} e ^{2} d ^{8}}{2 ^{3} e ^{3}}

Aplicar las leyes de los exponentes:

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

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

= \frac{e ^{2} d ^{8}}{2 ^{3 - 2} e ^{3}}

Restar:

3 - 2 = 1

= \frac{e ^{2} d ^{8}}{2 e ^{3}}

Aplicar las leyes de los exponentes:

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

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

= \frac{d ^{8}}{2 e ^{3 - 2}}

Restar:

3 - 2 = 1

= \frac{d ^{8}}{2 e}

e^{- \frac{x}{y}}

π \cdot 2^{2} \cdot 2

e^{- 8000}

e^{- \frac{1 ^{2}}{2}}

e^{- x^{2}} \times e^{x^{2}}