​$$\text{Find the value of } \left(\frac{1}{3}\right)^{-3} + \left(\frac{1}{9}\right)^{-3} + \left(\frac{1}{4}\right)^{-3}.$$​​

Correct option is D

Given:

​$$\left( \frac{1}{3} \right)^{-3} + \left( \frac{1}{9} \right)^{-3} + \left( \frac{1}{4} \right)^{-3}$$​

Formula Used:

​$$a^{-n} = \frac{1}{a^n}$$​

Solution:

​$$\left( \frac{1}{3} \right)^{-3} + \left( \frac{1}{9} \right)^{-3} + \left( \frac{1}{4} \right)^{-3} \\ \ \\=\left( 3 \right)^{3} +\left( 9 \right)^{3}+\left( 4 \right)^{3}\\ \ \\= 27 + 729 + 64 = 820$$​​

So, the value of the given expression is 820.