Problem 113 - College Algebra Essentials

Question

Use the order of operations to simplify each expression. $$\frac{5 \cdot 2-3^{2}}{\left[3^{2}-(-2)\right]^{2}}$$

Step-by-Step Solution

Answer

The simplified resulting value of the expression is \(\frac{1}{121}\)

Step 1: Apply the indices

Before dealing with any other operations, indices (exponents) should be dealt with first. Hence, replace \(3^{2}\) with 9 in both numerator and denominator. We now have: \[\frac{5 \cdot 2-9}{(9-(-2))^{2}}\]

Step 2: Execution of multiplication in the numerator and addition in the denominator

We need to perform the multiplication operation in the numerator and the addition operation in the denominator before subtraction: \[\frac{10-9}{(9+2)^{2}} = \frac{1}{11^{2}} \]

Step 3: Apply exponent in the denominator

Next, apply the exponent in the denominator: \[\frac{1}{121} \]