Question

use the order of operations to simplify:
a) ( 5^2 - 45 div 3^2 cdot 5 - 5 = \boxed{-5} )
b) ( \frac{7 cdot 2 - 3^2}{3^2 - (-2)^2} = square )
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Explanation:

Step1: Simplify numerator and denominator separately.

First, handle the numerator: \(7 \cdot 2 - 3^2\). Calculate exponents first: \(3^2 = 9\), then multiplication: \(7 \cdot 2 = 14\). Now subtract: \(14 - 9 = 5\).
Next, handle the denominator: \([3^2 - (-2)]^2\). Calculate the inner part first: \(3^2 = 9\), then \(9 - (-2) = 9 + 2 = 11\). Now square the result: \(11^2 = 121\).

Step2: Divide the numerator by the denominator.

Now we have \(\frac{5}{121}\) (since numerator is 5 and denominator is 121).

Answer:

\(\frac{5}{121}\)