​$$\textit{The value of} \left(\frac{15625}{49}\right)^{-\left(\frac{3}{2}\right)} \times \left(\frac{5}{7}\right)^5 \div \sqrt[4]{(625)^{-3}} \quad \text{is:}$$​

Correct option is C

Given:

​$$\left(\frac{15625}{49}\right)^{-\left(\frac{3}{2}\right)} \times \left(\frac{5}{7}\right)^5 \div \sqrt[4]{(625)^{-3}}$$

Solution:

$$\left( \frac{15625}{49} \right)^{-\frac{3}{2}} \times \left( \frac{5}{7} \right)^5 \div \sqrt[4]{(625)^{-3}}$$

$$=\frac {(7^2)^{\frac 32}}{(125^2)^{\frac 32}} \times \frac {5^5}{7^5}\div$$$$(5^4)^{-\frac{3}{4}}$$

=$$\frac{7^3}{125^3}\times \frac {5^5}{7^5}\div \frac 1{5^3}$$

=$$\frac{7^3}{(5^3)^3}\times \frac {5^5}{7^5}\times 5^3$$

=$$\frac {7^3\times 5^{5+3}}{5^9\times 7^5}$$

= $$\frac{1}{5^{9-8}\times7^{5-3}}$$​​

=$$\frac{1}{5\times 7^2}$$​​​

=$$\frac 1{245}$$