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Popular Álgebra >

simplificar (2a^2b^3c^4)^3(-3ab)^2(-b^3c)^3

Solução

simplificar

(2 a^{2} b^{3} c^{4})^{3} (- 3 ab)^{2} (- b^{3} c)^{3}

Solução

- 72 a^{8} b^{20} c^{15}

Passos da solução

(2 a^{2} b^{3} c^{4})^{3} (- 3 ab)^{2} (- b^{3} c)^{3}

Simplificar

(2 a^{2} b^{3} c^{4})^{3} : 8 a^{6} b^{9} c^{12}

= 8 a^{6} b^{9} c^{12} (- 3 ab)^{2} (- b^{3} c)^{3}

Simplificar

(- 3 ab)^{2} : 9 a^{2} b^{2}

= 8 a^{6} b^{9} c^{12} \cdot 9 a^{2} b^{2} (- b^{3} c)^{3}

Simplificar

(- b^{3} c)^{3} : - b^{9} c^{3}

= 8 a^{6} b^{9} c^{12} \cdot 9 a^{2} b^{2} (- b^{9} c^{3})

Aplique a regra:

a (- b) = - ab

8 a^{6} b^{9} c^{12} \cdot 9 a^{2} b^{2} (- b^{9} c^{3}) = - 8 a^{6} b^{9} c^{12} \cdot 9 a^{2} b^{2} b^{9} c^{3}

= - 8 a^{6} b^{9} c^{12} \cdot 9 a^{2} b^{2} b^{9} c^{3}

Multiplicar os números:

- 8 \cdot 9 = - 72

= - 72 a^{6} b^{9} c^{12} a^{2} b^{2} b^{9} c^{3}

Simplificar

a^{6} a^{2} : a^{8}

= - 72 a^{8} b^{9} c^{12} b^{2} b^{9} c^{3}

Simplificar

b^{9} b^{2} b^{9} : b^{20}

= - 72 a^{8} b^{20} c^{12} c^{3}

Simplificar

c^{12} c^{3} : c^{15}

= - 72 a^{8} b^{20} c^{15}

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