Question

please solve both questions ASAP​

Answer 1

$1) \: 5 \sqrt[3]{(16)} - 2 \sqrt[3]{(54)}$

$= 5 \times {16}^{ \frac{1}{3} } - 2 \times {54}^{ \frac{1}{3} }$

$= 5 \times ( {2}^{3} \times 2) {}^{ \frac{1}{3} } - 2 \times ( {3}^{3} \times 2) {}^{ \frac{1}{3} }$

$= 5 \times ( {2}^{3 \times \frac{1}{3} } \times {2}^{ \frac{1}{3} } ) - 2 \times ( {3}^{3 \times \frac{1}{3} } \times 2 {}^{ \frac{1}{3} } )$

$= 5 \times 2 \times {2}^{ \frac{1}{3} } - 2 \times 3 \times {2}^{ \frac{1}{3} }$

$= 10 \sqrt[3]{2} - 6 \sqrt[3]{2}$

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

$2) \: 5 \sqrt[3]{54} - 2 \sqrt[3]{16} + 4 \sqrt[3]{686}$

$= 5 \times {54}^{ \frac{1}{3} } - 2 \times {16}^{ \frac{1}{3} } + 4 \times {686}^{ \frac{1}{3} }$

$= 5 \times ( {3}^{3} \times 2) {}^{ \frac{1}{3} } - 2 \times ( {2}^{3} \times 2) {}^{ \frac{1}{3} } + 4 \times ( {7}^{3} \times 2) {}^{ \frac{1}{3} }$

$= 5 \times ( {3}^{3 \times \frac{1}{3} } \times 2 {}^{ \frac{1}{3} } ) - 2 \times ( {2}^{3 \times \frac{1}{3} } \times {2}^{ \frac{1}{3} } ) + 4 \times ( {7}^{3} \times {2}^{ \frac{1}{3} } )$

$= 5 \times 3 \times {2}^{ \frac{1}{3} } - 2 \times 2 \times {2}^{ \frac{1}{3} } + 4 \times 7 \times {2}^{ \frac{1}{3} }$

$= 15 \sqrt[3]{2} - 4 \sqrt[3]{2} + 28 \sqrt[3]{2}$

$= 43 \sqrt[3]{2} - 4 \sqrt[3]{2}$

$= 39 \sqrt[3]{2}$