Final answer:
To solve the expression, you can use the order of operations. The result of -1/5 times the quantity 3 minus 12 times the quantity one third squared is -1/3.
Step-by-step explanation:
To solve the expression, we'll follow the order of operations (PEMDAS/BODMAS). First, let's simplify the expression inside the parentheses.
The quantity one third squared = (1/3)^2 = 1/9
Next, we'll substitute the simplified expression into the main expression.
-1/5 * (3 - 12 * (1/9))
Simplifying further,
-1/5 * (3 - 12/9)
-1/5 * (3 - 4/3)
-1/5 * (9/3 - 4/3)
-1/5 * (5/3)
Finally, multiplying the fractions,
-1/5 * 5/3
(-1*5)/(5*3)
-1/3