Final answer:
To evaluate |(-12)^3 ÷ (14)^2|, we raise -12 to the third power, square 14, divide the two results, and then take the absolute value, which results in 8.82.
Step-by-step explanation:
To evaluate the expression |(-12)^3 ÷ (14)^2|, we need to follow the order of operations, raise each number to its respective power, divide, and take the absolute value. First, we raise -12 to the third power, which gives us -1728 because a negative number raised to an odd power results in a negative number. Then, we raise 14 to the second power (or square it), resulting in 196. To divide, we take the absolute value of -1728 and divide it by 196, which equals 8.82 (approximately). However, before performing the division, we must remember that when using absolute value, we take the non-negative value of a number. Thus, the absolute value of -1728 is 1728. So the correct division is 1728 ÷ 196, which equals 8.82 (rounded to two decimal places). Finally, the absolute value of 8.82 is also 8.82 since it is already a non-negative number.