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simplificar (((3a^3b^2)^2)^{-5})^{-3}

Solução

simplificar

(((3 a^{3} b^{2})^{2})^{- 5})^{- 3}

3^{30} a^{90} b^{60}

Passos da solução

(((3 a^{3} b^{2})^{2})^{- 5})^{- 3}

((3 a^{3} b^{2})^{2})^{- 5} : (3 a^{3} b^{2})^{- 10}

= ((3 a^{3} b^{2})^{- 10})^{- 3}

(3 a^{3} b^{2})^{- 10} = \frac{1}{3 ^{10} a ^{30} b ^{20}}

= (\frac{1}{3 ^{10} a ^{30} b ^{20}})^{- 3}

Aplicar as propriedades dos expoentes:

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

= \frac{1}{( \frac{1}{3 ^{10} a ^{30} b ^{20}} ) ^{3}}

Aplicar as propriedades dos expoentes:

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

(\frac{1}{3 ^{10} a ^{30} b ^{20}})^{3} = \frac{1 ^{3}}{( 3 ^{10} a ^{30} b ^{20} ) ^{3}}

= \frac{1}{\frac{1 ^{3}}{( 3 ^{10} a ^{30} b ^{20} ) ^{3}}}

Aplicar as propriedades dos expoentes:

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

(3^{10} a^{30} b^{20})^{3} = (3^{10})^{3} (a^{30})^{3} (b^{20})^{3}

= \frac{1}{\frac{1 ^{3}}{( 3 ^{10} ) ^{3} ( a ^{30} ) ^{3} ( b ^{20} ) ^{3}}}

(3^{10})^{3} : 3^{30}

= \frac{1}{\frac{1 ^{3}}{3 ^{30} ( a ^{30} ) ^{3} ( b ^{20} ) ^{3}}}

(a^{30})^{3} : a^{90}

= \frac{1}{\frac{1 ^{3}}{3 ^{30} a ^{90} ( b ^{20} ) ^{3}}}

(b^{20})^{3} : b^{60}

= \frac{1}{\frac{1 ^{3}}{3 ^{30} a ^{90} b ^{60}}}

Aplicar as propriedades das frações:

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

= \frac{3 ^{30} a ^{90} b ^{60}}{1 ^{3}}

Aplicar a regra

1^{a} = 1

1^{3} = 1

= \frac{3 ^{30} a ^{90} b ^{60}}{1}

Aplicar as propriedades das frações:

\frac{a}{1} = a

= 3^{30} a^{90} b^{60}

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