Final answer:
The expression negative one sixth times the quantity 3 minus 15 times the quantity one third squared simplifies to -2/9. The steps include squaring one third, multiplying by 15, and finally multiplying by negative one sixth.
Step-by-step explanation:
The question asks us to calculate the value of negative one sixth times the quantity 3 minus 15 times the quantity one third squared. First, we will simplify the expression inside the parentheses. One third squared is (1/3)² which is 1/9. So, the expression becomes 3 - 15*(1/9). Multiplying 15 by 1/9 gives us 15/9, which simplifies to 5/3. Therefore, 3 - 5/3 turns into 9/3 - 5/3, which simplifies to 4/3.
Now we multiply 4/3 by -1/6. Multiplying these two gives -4/18, which simplifies to -2/9. This is the final answer.