Problem 114 - Algebra and Trigonometry

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: Handle the Numerator

The numerator consists of division and multiplication operations. Following the order of operations, it simplifies to \(5+12=17.\)

Step 2: Handle the Parentheses and Exponents in the Denominator

The denominator requires simplifying an expression in parentheses and applying the exponent. The expression in the parentheses simplifies to \(12-6=6\). Then, squaring gives \(6^2=36.\)

Step 3: Divide the Numerator by the Denominator

Finally, divide the numerator \(17\) by the denominator \(36\) to obtain the simplified expression, \( \frac{17}{36} \).