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Popular Álgebra >

expandir {5(2x^2z^4)^3(x^3y^3)^2}^2

Solução

expandir

{5 (2 x^{2} z^{4})^{3} (x^{3} y^{3})^{2}}^{2}

Solução

1600 x^{24} z^{24} y^{12}

Passos da solução

(5 (2 x^{2} z^{4})^{3} (x^{3} y^{3})^{2})^{2}

Simplificar

5 (2 x^{2} z^{4})^{3} (x^{3} y^{3})^{2} : 2^{3} \cdot 5 x^{12} z^{12} y^{6}

= (2^{3} \cdot 5 x^{12} z^{12} y^{6})^{2}

Aplicar as propriedades dos expoentes:

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

= 5^{2} (2^{3})^{2} (y^{6})^{2} (z^{12})^{2} (x^{12})^{2}

(2^{3})^{2} : 2^{6}

= 5^{2} \cdot 2^{6} (z^{12})^{2} (x^{12})^{2} (y^{6})^{2}

(z^{12})^{2} : z^{24}

= 5^{2} \cdot 2^{6} z^{24} (x^{12})^{2} (y^{6})^{2}

(x^{12})^{2} : x^{24}

= 5^{2} \cdot 2^{6} z^{24} x^{24} (y^{6})^{2}

(y^{6})^{2} : y^{12}

= 5^{2} \cdot 2^{6} z^{24} x^{24} y^{12}

Simplificar

= 1600 x^{24} z^{24} y^{12}

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