$\left(\frac{4}{5}\right)^{-2}-\left(\frac{2^{-2}}{3}\right)$

Step 1 ：First, we need to calculate the value of \(\left(\frac{4}{5}\right)^{-2}\) and \(\left(\frac{2^{-2}}{3}\right)\) separately.

Step 2 ：The negative exponent means that we need to take the reciprocal of the base. So, \(\left(\frac{4}{5}\right)^{-2}\) is equivalent to \(\left(\frac{5}{4}\right)^{2}\).

Step 3 ：Similarly, \(\left(\frac{2^{-2}}{3}\right)\) is equivalent to \(\left(\frac{1}{2^{2}}\right)/3\).

Step 4 ：After calculating these values, we get first_value = 1.5625 and second_value = 0.08333333333333333.

Step 5 ：We can subtract the second value from the first one to get the final answer: final_answer = 1.4791666666666667.

Step 6 ：Final Answer: The final answer is \(\boxed{1.4791666666666667}\).