The value of $$\left(\frac{64}{25}\right)^{-\frac{3}{2}} \times \left(\frac{2}{5}\right)^4 \div \sqrt[5]{(32)^{-3}}$$​ is:

Correct option is B

Given:

​$$\left(\frac{64}{25}\right)^{-\frac{3}{2}} \times \left(\frac{2}{5}\right)^4 \div \sqrt[5]{(32)^{-3}}$$​​

Formula Used:

​$$x^{-a} =\frac{1}{x^a}$$​​

Solution:

​$$\left(\frac{64}{25}\right)^{-\frac{3}{2}} \times \left(\frac{2}{5}\right)^4 \div \sqrt[5]{(32)^{-3}}$$​​

=$$\left(\frac{25}{64}\right)^{\frac{3}{2}} \times \left(\frac{2^4}{5^4}\right) \div \left(\frac{1}{\sqrt[5]{(32)^3}}\right)$$​​

=$$\left(\frac{5}{8}\right)^3 \times \left(\frac{16}{625}\right) \div \left(\frac{1}{(32)^{\frac{3}{5}}}\right)$$​​

=$$\left(\frac{125}{512}\right) \times \left(\frac{16}{625}\right) \div \left(\frac{1}{(8)}\right)$$​​

=$$\left(\frac{125}{512}\right) \times \left(\frac{16}{625}\right) \times 8$$​​

​$$= \frac{1}{20}$$​​