Let's break this down step by step:
1) ((2/5)^-1)^2 = (5/2)^2 = 25/4
2) 3^-9 * 3^12 = 3^3 = 27
3) 6^-7 : 6^-9 = 6^2 = 36
Now we can plug these values back into the original expression:
25/4 + 27 - 36 = 25/4 + 27 - 36Converting 27 and 36 to fractions:25/4 + 108/4 - 144/4
Combining like terms:25/4 + 108/4 - 144/4 = -11/4
Therefore, the final answer is -11/4.
Let's break this down step by step:
1) ((2/5)^-1)^2 = (5/2)^2 = 25/4
2) 3^-9 * 3^12 = 3^3 = 27
3) 6^-7 : 6^-9 = 6^2 = 36
Now we can plug these values back into the original expression:
25/4 + 27 - 36 = 25/4 + 27 - 36
Converting 27 and 36 to fractions:
25/4 + 108/4 - 144/4
Combining like terms:
25/4 + 108/4 - 144/4 = -11/4
Therefore, the final answer is -11/4.