Question

simplificar: (8∛2 .3∛8)/(2∛4)

Answer 1

Respuesta:

Explicación paso a paso:

(8∛2 .3∛8)/(2∛4)

$\frac{24\sqrt[3]{2*8} }{2\sqrt[3]{4} } \\12\sqrt[3]{\frac{16}{4} } \\12\sqrt[3]{4}$

Answer 2

Respuesta:

$6\sqrt[3]{2}\cdot \:4^{\frac{2}{3}}$

Explicación paso a paso:

$\frac{8\sqrt[3]{2}\cdot \:3\sqrt[3]{8}}{2\sqrt[3]{4}}$

• 8×3=24

$=\frac{24\sqrt[3]{2}\sqrt[3]{8}}{2\sqrt[3]{4}}$

• $\frac{24}{2}=12$

$=\frac{12\sqrt[3]{2}\sqrt[3]{8}}{\sqrt[3]{4}}$

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$12\sqrt[3]{2}\sqrt[3]{8}\\=2^2\cdot \:3\sqrt[3]{2}\sqrt[3]{8}\\=2^2\cdot \:3\sqrt[3]{2}\cdot \:2^{3\cdot \frac{1}{3}}\\=2^2\cdot \:3\sqrt[3]{2}\cdot \:2\\=3\sqrt[3]{2}\cdot \:2^{2+1}\\=3\sqrt[3]{2}\cdot \:2^3$

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$=\frac{2^3\cdot \:3\sqrt[3]{2}}{\sqrt[3]{4}}$

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$3\sqrt[3]{2}\cdot \:2^3\\=3\cdot \:8\sqrt[3]{2}\\=24\sqrt[3]{2}$

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$=\frac{24\sqrt[3]{2}}{\sqrt[3]{4}}$

$=\frac{24\sqrt[3]{2}\cdot \:4^{\frac{2}{3}}}{\sqrt[3]{4}\cdot \:4^{\frac{2}{3}}}$

$\sqrt[3]{4}\cdot \:4^{\frac{2}{3}}=4$

$=\frac{24\sqrt[3]{2}\cdot \:4^{\frac{2}{3}}}{4}$

$=6\sqrt[3]{2}\cdot \:4^{\frac{2}{3}}$