Final answer:
The value of the expression [2−|−−14−2(−35)|]÷(−6) is −7/3 after performing operations inside the absolute value, simplifying, and dividing by −6.
Step-by-step explanation:
To evaluate the expression [2−|−−14−2(−35)|]÷(−6), we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, inside the absolute value, we need to perform the multiplication: 2(−35) = 2 * 35 = 70. Now our expression is 2−|−14−70|.
Next, continue inside the absolute value, we handle the subtraction: −14−70 = −14 + (-70) = −84. So our expression becomes 2−| −84 |.
The absolute value of −84 is 84, so now we have 2−84 = 2 + (-84) = −82.
Finally, we divide by −6: −82 ÷ (−6) = −82/(-6) = 14/6 = 7/3 after simplification.
Therefore, the value of the expression is −7/3 as a simplified fraction.