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simplificar (((3x^3)^2)^{-5})^{-2}

Solución

simplificar

(((3 x^{3})^{2})^{- 5})^{- 2}

3^{20} x^{60}

Pasos de solución

(((3 x^{3})^{2})^{- 5})^{- 2}

((3 x^{3})^{2})^{- 5} : (3 x^{3})^{- 10}

= ((3 x^{3})^{- 10})^{- 2}

(3 x^{3})^{- 10} = \frac{1}{3 ^{10} x ^{30}}

= (\frac{1}{3 ^{10} x ^{30}})^{- 2}

Aplicar las leyes de los exponentes:

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

= \frac{1}{( \frac{1}{3 ^{10} x ^{30}} ) ^{2}}

Aplicar las leyes de los exponentes:

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

(\frac{1}{3 ^{10} x ^{30}})^{2} = \frac{1 ^{2}}{( 3 ^{10} x ^{30} ) ^{2}}

= \frac{1}{\frac{1 ^{2}}{( 3 ^{10} x ^{30} ) ^{2}}}

Aplicar las leyes de los exponentes:

(a \cdot b)^{n} = a^{n} b^{n}

(3^{10} x^{30})^{2} = (3^{10})^{2} (x^{30})^{2}

= \frac{1}{\frac{1 ^{2}}{( 3 ^{10} ) ^{2} ( x ^{30} ) ^{2}}}

(3^{10})^{2} : 3^{20}

= \frac{1}{\frac{1 ^{2}}{3 ^{20} ( x ^{30} ) ^{2}}}

(x^{30})^{2} : x^{60}

= \frac{1}{\frac{1 ^{2}}{3 ^{20} x ^{60}}}

Aplicar las propiedades de las fracciones:

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

= \frac{3 ^{20} x ^{60}}{1 ^{2}}

Aplicar la regla

1^{a} = 1

1^{2} = 1

= \frac{3 ^{20} x ^{60}}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

= 3^{20} x^{60}

x - 14 x + 14

(2.3 x^{103}) (4 x^{105})

e^{- x l n (1 + e^{y})}

48 e^{- 0.1724}

\frac{e ^{- 10 x}}{e ^{- 100 x}}