Question

use the order of operations to find the value of the following expression.\\(\frac{16div4cdot4|3^{2}+1^{2}|}{7 + 9 - 6^{2}}\\)\\(\frac{16div4cdot4|3^{2}+1^{2}|}{7 + 9 - 6^{2}}=\boxed{\frac{36}{5}}\\)\\(\text{(simplify your answer. type an integer or a fraction.)}\\)

Explanation:

Step1: Evaluate exponents inside absolute value

$3^2=9$, $1^2=1$

Step2: Sum inside absolute value

$|9+1|=|10|=10$

Step3: Simplify numerator operations

$16 - 4 \cdot 4 \cdot 10 = 16 - 160 = -144$

Step4: Evaluate exponent in denominator

$6^2=36$

Step5: Simplify denominator operations

$7 + 9 - 36 = 16 - 36 = -20$

Step6: Simplify the fraction

$\frac{-144}{-20} = \frac{36}{5}$

Answer:

$\frac{36}{5}$