Problem 120 - College Algebra Essentials

Question

Use the order of operations to simplify each expression. $$\frac{12 \div 3 \cdot 5\left|2^{2}+3^{2}\right|}{7+3-6^{2}}$$

Step-by-Step Solution

Answer

The simplified result of the expression given is -10.

Step 1: Solve the expression inside the absolute value

The expression inside the absolute value is \(2^{2} + 3^{2}\). So, calculate the squares first, which gives us \(4 + 9 = 13\). The absolute value of 13 is 13.

Step 2: Solve the multiplication and division in the numerator

The numerator is \(12 \div 3 \cdot 5 \cdot 13\). Following the order of operations, the division is carried out first. So, \(12 \div 3 = 4\), which results in \(4 \cdot 5 \cdot 13\). Then carry out the multiplication operations \(4 * 5 = 20\) and \(20 * 13 = 260\). Therefore, the value of the numerator is 260.

Step 3: Solve the addition and subtraction in the denominator

The denominator is \(7 + 3 - 6^{2}\). According to order of operations, the operation of exponentiation is performed first: \(6^{2} = 36\), which results in \(7 + 3 - 36\). Then follow with the operation of addition: \(7 + 3 = 10\), leading to \(10 - 36\). Finally the subtraction: \(10 - 36 = -26\). Therefore, the value of the denominator is -26.

Step 4: Carry out the division

Now carry out the division with the values obtained for the numerator and the denominator, which is \(260 \div -26 = -10\)