​$$\text{Find the value of } \left(\frac{1}{5}\right)^{-4} + \left(\frac{1}{9}\right)^{-4} + \left(\frac{1}{2}\right)^{-4}.$$​​

Correct option is A

Given:

​$$\left(\frac{1}{5}\right)^{-4} + \left(\frac{1}{9}\right)^{-4} + \left(\frac{1}{2}\right)^{-4}.$$

Formula Used:

a^-n = $$\left(\frac 1a\right)^n$$

Solution:

​$$\left(\frac{1}{5}\right)^{-4} + \left(\frac{1}{9}\right)^{-4} + \left(\frac{1}{2}\right)^{-4}$$

= 5⁴ + 9⁴ + 2⁴​

= 625 + 6561 + 16

= 7202