Simplify:

​​​$$\left(\frac{1}{512}\right)^{\frac{-2}{3}} \div \left(\frac{1}{64}\right)^{\frac{-4}{3}}$$​​

Correct option is C

Given:

​$$\left(\frac{1}{512}\right)^{\frac{-2}{3}} \div \left(\frac{1}{64}\right)^{\frac{-4}{3}}$$​​

Formula Used:

​$$\frac{1}{x^{-a}}=x^a$$​​

​$$x^{\frac{1}{3}} = \sqrt[3]{x}$$​​

Solution:

​$$\left(\frac{1}{512}\right)^{\frac{-2}{3}} \div \left(\frac{1}{64}\right)^{\frac{-4}{3}}$$​​

​$$512^{\frac{2}{3}} \div 64^{\frac{4}{3}}$$​​

​$$( \sqrt[3]{512})^2 \div ( \sqrt[3]{64})^4$$​​

​$$8^2 \div 4^4$$​​

​$$=\frac{64}{256}$$​​

​$$= \frac{1}{4}$$​​