Question

Calcula el valor de las siguientes expresiones​

Answer 1

Explicación paso a paso:

(A)

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$\frac{ \sqrt[3]{ {x}^{20} } }{ \sqrt[3]{ {x}^{2} } } = \sqrt[3]{ {x}^{20} \div {x}^{2} } \\ \\ \frac{ \sqrt[3]{ {x}^{20} } }{ \sqrt[3]{ {x}^{2} } } = \sqrt[3]{ {x}^{(20 - 2)} } \\ \\ \frac{ \sqrt[3]{ {x}^{20} } }{ \sqrt[3]{ {x}^{2} } } = \sqrt[3]{ {x}^{18} } \\ \\ \frac{ \sqrt[3]{ {x}^{20} } }{ \sqrt[3]{ {x}^{2} } } = {x}^{(18 \div 3)} \\ \\ \frac{ \sqrt[3]{ {x}^{20} } }{ \sqrt[3]{ {x}^{2} } } = {x}^{6}$

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(B)

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$\frac{ \sqrt[6]{ {x}^{31} } }{ \sqrt[6]{ {x}^{1} } } = \sqrt[6]{ {x}^{31} \div {x}^{1} } \\ \\ \frac{ \sqrt[6]{ {x}^{31} } }{ \sqrt[6]{ {x}^{1} } } = \sqrt[6]{ {x}^{(31 - 1)} } \\ \\ \frac{ \sqrt[6]{ {x}^{31} } }{ \sqrt[6]{ {x}^{1} } } = \sqrt[6]{ {x}^{30} } \\ \\ \frac{ \sqrt[6]{ {x}^{31} } }{ \sqrt[6]{ {x}^{1} } } = {x}^{(30 \div 6)} \\ \\ \frac{ \sqrt[6]{ {x}^{31} } }{ \sqrt[6]{ {x}^{1} } } = {x}^{5}$