Question

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Answer 1

$\huge\mathbb{A~N~S~W~E~R}$

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$= 10 \div {8}^{ \frac{ - 1}{3} } \\ \\ = 10 \div {(2)}^{3 \times \frac{ - 1}{3} } \\ \\ = 10 \div {2}^{( - 1)} \\ \\ = \frac{10}{ {2}^{ - 1} } \\ \\ = 10 \times {2}^{1} \\ \\ = 20$

${\large\color{Red}{Answer~is~20~. }}$

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Answer 2

ANSWER: 20

Method is given below.

$\mathsf{10 \div 8^{\frac{-1}{3}}} \\ \\ \\ \mathsf{10 \div 8^{\frac{1}{3} \times -1}} \\ \\ \\ \mathsf{10 \div \left(8^{\frac{1}{3}\right)^{-1}}} \\ \\ \\ \mathsf{10 \div \left(\mathsf{\sqrt[3]{8}}\right)^{-1}} \\ \\ \\ \mathsf{10 \div 2^{-1}} \\ \\ \\ \mathsf{10 \times (2^{-1})^{-1}} \\ \\ \\ \mathsf{10 \times 2^{-1 \times -1}} \\ \\ \\ \mathsf{10 \times 2^1} \\ \\ \\ \mathsf{10 \times 2} \\ \\ \\ \Large \textsf{20}$

First we have to simplify the exponential form, i.e., 8^(-1/3).

On simplifying we get it as 2^(-1), which values 1/2.

According to  a ÷ b = a × 1/b = a × b^(-1),  

10 ÷ 2^(-1)  becomes  10 × (2^(-1))^(-1) =  10 × 2 = 20.

Thus we get the answer 20.