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1. What will come in place of both the question marks in the following question : $\frac{{(?)}^{\frac{2}{3}}}{42} = \frac{5}{{(?)}^{\frac{1}{3}}}$

A. 10

B. $10 \sqrt{2}$

C. $\sqrt{20}$

D. 20

Solution:

\begin{aligned} Let \frac{{(x)}^{\frac{2}{3}}}{42} = \frac{5}{{(x)}^{\frac{1}{3}}} \\ Then, \\ x^{\frac{2}{3}} . x^{\frac{1}{3}} = 42 \times 5 \\ = 210 \\ \Rightarrow x^{(\frac{2}{3} + \frac{1}{3})} = 210 \\ \Rightarrow x = 210 \end{aligned}

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