​$$\textit{The value of} \left(\frac{4096}{9}\right)^{-\left(\frac{3}{2}\right)} \times \left(\frac{4}{3}\right)^5 \div \sqrt[4]{(256)^{-3}} \quad \text{is:}$$​​

Correct option is A

Given:

$$\left( \frac{4096}{9} \right)^{-\frac{3}{2}} \times \left( \frac{4}{3} \right)^5 \div \sqrt[4]{(256)^{-3}}$$

Solution:

​$$\left( \frac{4096}{9} \right)^{-\frac{3}{2}} \times \left( \frac{4}{3} \right)^5 \div \sqrt[4]{(256)^{-3}}$$

$$=\frac {(3^2)^{\frac 32}}{(64^2)^{\frac 32}} \times \frac {4^5}{3^5}\div$$$$(4^4)^{-\frac{3}{4}}$$

=$$\frac{3^3}{64^3}\times \frac {4^5}{3^5}\div \frac 1{4^3}$$

=$$\frac{3^3}{(4^3)^3}\times \frac {4^5}{3^5}\times4^3$$

=$$\frac {3^3\times 4^8}{4^9\times 3^5}$$

= $$\frac{1}{4^{9-8}\times3^{5-3}}$$​​

=$$\frac{1}{4\times 3^2}$$​​​

=$$\frac 1{36}$$