Question

now we will use the whole hierarchy to evaluate some expressions. grouping: let’s begin our study of ‘grouping.’ remember that we did not want to limit ourselves to parentheses, because there are so many other grouping symbols like brackets and braces { }. parentheses, brackets, and braces work the same. you perform the expression inside of these symbols first. it gets tricky when the grouping is implied like in a fraction. consider $\frac{3 - 8cdot3}{3 + 4}=\frac{(3 - 8cdot3)}{(3 + 4)}=(3 - 8cdot3)div(3 + 4)$ when you encounter a fraction, you must perform any operations in the numerator and denominator first. then perform the division. evaluate each of the following expressions using the order of operations. ex 10. $7(8 - 5)$ ex 11. $3cdot16div4 - 3$ ex 12. $4 + 9-6^{2}-7$ ex 13. $2(3 - 7)^{2}div2$

Explanation:

Step1: Evaluate Ex 10

First, solve inside - parentheses: $8 - 5=3$. Then multiply: $7\times3 = 21$.

Step2: Evaluate Ex 11

First, multiply: $3\times16 = 48$. Then divide: $48\div4 = 12$. Finally, subtract: $12-3 = 9$.

Step3: Evaluate Ex 12

First, calculate the exponent: $6^{2}=36$. Then add and subtract from left - to - right: $4 + 9=13$, $13-36=-23$, $-23-7=-30$.

Step4: Evaluate Ex 13

First, solve inside - parentheses: $3 - 7=-4$. Then calculate the exponent: $(-4)^{2}=16$. Next, multiply: $2\times16 = 32$. Finally, divide: $32\div2 = 16$.

Answer:

Ex 10: 21
Ex 11: 9
Ex 12: - 30
Ex 13: 16