examples 1 - 3 evaluate each expression. 1. $9^{2}$ 4. $30 - 14div2$ 7. $8(2)-4^{2}+7(4)$ 2. $4^{4}$ 5. $5cdot5 - 1cdot3$ 8. $\frac{11 - 8}{1+7cdot2}$ 3. $3^{5}$ 6. $(2 + 5)4$ 9. $\frac{(4cdot3)^{2}}{9 + 3}$ example 4 evaluate each expression if $a = 4$, $b = 6$, and $c = 8$. 10. $8b - a$ 11. $2a+(b^{2}div3)$ 12. $\frac{b(9 - c)}{a^{2}}$

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Accepted Answer

1. **For $9^{2}$**:
   - # Explanation:
     - ## Step1: Recall exponent - meaning
       $9^{2}=9\times9$
     - ## Step2: Calculate product
       $9\times9 = 81$
   - # Answer:
     $81$
2. **For $4^{4}$**:
   - # Explanation:
     - ## Step1: Recall exponent - meaning
       $4^{4}=4\times4\times4\times4$
     - ## Step2: Calculate $4\times4 = 16$
       $4\times4\times4\times4=16\times4\times4$
     - ## Step3: Calculate $16\times4 = 64$
       $16\times4\times4 = 64\times4$
     - ## Step4: Calculate $64\times4$
       $64\times4=256$
   - # Answer:
     $256$
3. **For $3^{5}$**:
   - # Explanation:
     - ## Step1: Recall exponent - meaning
       $3^{5}=3\times3\times3\times3\times3$
     - ## Step2: Calculate $3\times3 = 9$
       $3\times3\times3\times3\times3=9\times3\times3\times3$
     - ## Step3: Calculate $9\times3 = 27$
       $9\times3\times3\times3=27\times3\times3$
     - ## Step4: Calculate $27\times3 = 81$
       $27\times3\times3=81\times3$
     - ## Step5: Calculate $81\times3$
       $81\times3 = 243$
   - # Answer:
     $243$
4. **For $30−14\div2$**:
   - # Explanation:
     - ## Step1: Follow order of operations (division first)
       $14\div2 = 7$
     - ## Step2: Subtract
       $30 - 7=23$
   - # Answer:
     $23$
5. **For $5\cdot5−1\cdot3$**:
   - # Explanation:
     - ## Step1: Follow order of operations (multiplication first)
       $5\cdot5 = 25$ and $1\cdot3 = 3$
     - ## Step2: Subtract
       $25-3 = 22$
   - # Answer:
     $22$
6. **For $(2 + 5)4$**:
   - # Explanation:
     - ## Step1: Calculate inside the parentheses
       $2 + 5=7$
     - ## Step2: Multiply
       $7\times4 = 28$
   - # Answer:
     $28$
7. **For $[8(2)-4^{2}]+7(4)$**:
   - # Explanation:
     - ## Step1: Calculate $8(2)=16$ and $4^{2}=16$
       $[8(2)-4^{2}]+7(4)=[16 - 16]+7(4)$
     - ## Step2: Calculate inside the brackets
       $16 - 16 = 0$
     - ## Step3: Calculate $7(4)=28$
       $0+28 = 28$
   - # Answer:
     $28$
8. **For $\frac{11 - 8}{1+7\cdot2}$**:
   - # Explanation:
     - ## Step1: Calculate numerator
       $11 - 8 = 3$
     - ## Step2: Calculate denominator (multiplication first)
       $7\cdot2 = 14$, then $1+14 = 15$
     - ## Step3: Divide
       $\frac{3}{15}=\frac{1}{5}=0.2$
   - # Answer:
     $0.2$
9. **For $\frac{(4\cdot3)^{2}}{9 + 3}$**:
   - # Explanation:
     - ## Step1: Calculate inside the parentheses
       $4\cdot3 = 12$
     - ## Step2: Calculate the square
       $(4\cdot3)^{2}=12^{2}=144$
     - ## Step3: Calculate the denominator
       $9 + 3=12$
     - ## Step4: Divide
       $\frac{144}{12}=12$
   - # Answer:
     $12$
10. **For $8b - a$ with $a = 4$ and $b = 6$**:
   - # Explanation:
     - ## Step1: Substitute values
       $8b - a=8\times6-4$
     - ## Step2: Multiply
       $8\times6 = 48$
     - ## Step3: Subtract
       $48-4 = 44$
   - # Answer:
     $44$
11. **For $2a+(b^{2}\div3)$ with $a = 4$ and $b = 6$**:
   - # Explanation:
     - ## Step1: Calculate $b^{2}$
       $b^{2}=6^{2}=36$
     - ## Step2: Calculate $b^{2}\div3$
       $36\div3 = 12$
     - ## Step3: Calculate $2a$
       $2a=2\times4 = 8$
     - ## Step4: Add
       $8 + 12=20$
   - # Answer:
     $20$
12. **For $\frac{b(9 - c)}{a^{2}}$ with $a = 4$, $b = 6$, and $c = 8$**:
   - # Explanation:
     - ## Step1: Calculate inside the parentheses
       $9 - c=9 - 8 = 1$
     - ## Step2: Calculate $b(9 - c)$
       $b(9 - c)=6\times1 = 6$
     - ## Step3: Calculate $a^{2}$
       $a^{2}=4^{2}=16$
     - ## Step4: Divide
       $\frac{6}{16}=\frac{3}{8}=0.375$
   - # Answer:
     $0.375$

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