simplificar [((7x^3yz^5)^6)/((49x^6y^2z^4)^3)]^4

Solução

simplificar

[\frac{( 7 x ^{3} y z ^{5} ) ^{6}}{( 49 x ^{6} y ^{2} z ^{4} ) ^{3}}]^{4}

z^{72}

Passos da solução

(\frac{( 7 x ^{3} y z ^{5} ) ^{6}}{( 49 x ^{6} y ^{2} z ^{4} ) ^{3}})^{4}

Aplicar as propriedades dos expoentes:

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

= \frac{( ( 7 x ^{3} y z ^{5} ) ^{6} ) ^{4}}{( ( 49 x ^{6} y ^{2} z ^{4} ) ^{3} ) ^{4}}

Simplificar

((7 x^{3} y z^{5})^{6})^{4} : 7^{24} x^{72} y^{24} z^{120}

= \frac{7 ^{24} x ^{72} y ^{24} z ^{120}}{( ( 49 x ^{6} y ^{2} z ^{4} ) ^{3} ) ^{4}}

Simplificar

((49 x^{6} y^{2} z^{4})^{3})^{4} : 4 9^{12} x^{72} y^{24} z^{48}

= \frac{7 ^{24} x ^{72} y ^{24} z ^{120}}{4 9 ^{12} x ^{72} y ^{24} z ^{48}}

Cancelar

\frac{7 ^{24} x ^{72} y ^{24} z ^{120}}{4 9 ^{12} x ^{72} y ^{24} z ^{48}} : \frac{7 ^{24} z ^{72}}{4 9 ^{12}}

= \frac{7 ^{24} z ^{72}}{4 9 ^{12}}

Fatorar

4 9^{12} : 7^{24}

= \frac{7 ^{24} z ^{72}}{7 ^{24}}

Eliminar o fator comum:

7^{24}

= z^{72}

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