Problem 119 - College Algebra Essentials

Question

Use the order of operations to simplify each expression. $$\frac{(5-6)^{2}-2|3-7|}{89-3 \cdot 5^{2}}$$

Step-by-Step Solution

Answer

-0.5

Step 1: Solve Inside Parentheses and Absolute Values

Calculate the values inside parentheses and the absolute value. So, you have \((5-6)^{2}\) which is \((-1)^{2}\) and gives 1. Also, you have \(|3-7|\), which is |-4| and gives 4.

Step 2: Calculate powers

Calculate the powers. In this case, we only have \(5^{2}\), which is \(25\).

Step 3: Perform Multiplication

Perform the multiplication operation. So, \(3 \cdot 25\) gives \(75\).

Step 4: Perform Subtraction

Perform the subtraction operation. So, in the numerator \(1-2*4\) gives \(-7\), and in the denominator \(89-75\) gives 14.

Step 5: Execute Division

Perform the division operation. So, \(-7/14\) gives \(-0.5\) or \(-1/2\).