Problem 114 - College Algebra Essentials

Question

Use the order of operations to simplify each expression. $$\frac{10 \div 2+3 \cdot 4}{(12-3 \cdot 2)^{2}}$$

Step-by-Step Solution

Answer

The simplified expression is \( \frac{17}{36} \).

Step 1: Simplify the expression in the numerator

First, solve the division and multiplication inside the numerator. According to PEMDAS/BODMAS rule, division and multiplication should be addressed from left to right. Thus, \(10 \div 2+3 \cdot 4\) becomes \(5+3 \cdot 4\), which simplifies to \(5+12=17\).

Step 2: Simplify the expression in the denominator

Next, solve for the expression inside the parentheses in the denominator: \(12-3 \cdot 2\). According to the order of operations, multiplication is performed before subtraction, which gives \(12-6=6\). Raise this result to the power of 2 \(\left(6^{2}\right)\) to get 36.

Step 3: Divide the results

The final step is to divide the resulted numerator and the resulted denominator. \( \frac{17}{36} \) is the simplified form of the original expression.