Question

order of operations homework
be sure to show all work and box/circle your answer.

1. $(64 - 2^{2})-(8 + 7)$
2. $(55 - 5)-2 - 3^{2}$
3. $(4cdot9 + 4^{2})-3$
4. $(7 + 2)^{2}+(20 - 10)$
5. $(32 - 2)-2 + 4^{2}$
6. $(37 - 3^{2})-(-1 + 5)$
7. $4cdot(11 - 6)+7^{2}$
8. $4cdot(9 + 3)+9^{2}$
9. $(11cdot5 + 5^{2})-5$
10. $8cdot(8 + 4)-5^{2}$
11. $(2 + 2)^{2}+(18 - 6)$
12. $6cdot(10 - 4)+7^{2}$

Explanation:

Step1: Calculate parentheses and exponents

For each expression, first handle operations inside parentheses and exponents.
For example, in \( (64 - 2^{2})-(8 + 7) \):

• Calculate \( 2^{2}=4 \) and \( 8 + 7=15 \)
• Then \( 64-4 = 60 \)

Step2: Perform subtraction

\( 60-15=45 \)

Another example, \( (4\cdot9 + 4^{2})-3 \):

• Calculate \( 4\cdot9=36 \), \( 4^{2}=16 \)
• Then \( 36 + 16=52 \)
• \( 52-3 = 49 \)

For \( (32-2)-2 + 4^{2} \):

• \( 32-2=30 \), \( 4^{2}=16 \)
• \( 30-2+16=44 \)

For \( 4\cdot(11 - 6)+7^{2} \):

• \( 11-6 = 5 \), \( 7^{2}=49 \)
• \( 4\cdot5+49=20 + 49=69 \)

For \( (11\cdot5+5^{2})-5 \):

• \( 11\cdot5=55 \), \( 5^{2}=25 \)
• \( 55 + 25=80 \), \( 80-5=75 \)

For \( (2 + 2)^{2}+(18 - 6) \):

• \( 2+2=4 \), \( 4^{2}=16 \), \( 18-6 = 12 \)
• \( 16+12=28 \)

For \( (55-5)-2-3^{2} \):

• \( 55-5=50 \), \( 3^{2}=9 \)
• \( 50-2-9=39 \)

For \( (7 + 2)^{2}+(20 - 10) \):

• \( 7+2=9 \), \( 9^{2}=81 \), \( 20-10 = 10 \)
• \( 81+10=91 \)

For \( (37-3^{2})-(-1 + 5) \):

• \( 3^{2}=9 \), \( -1+5=4 \)
• \( 37-9=28 \), \( 28-4=24 \)

For \( 4\cdot(9 + 3)+9^{2} \):

• \( 9+3=12 \), \( 9^{2}=81 \)
• \( 4\cdot12+81=48+81=129 \)

For \( 8\cdot(8 + 4)-5^{2} \):

• \( 8+4=12 \), \( 5^{2}=25 \)
• \( 8\cdot12-25=96-25=71 \)

For \( 6\cdot(10 - 4)+7^{2} \):

• \( 10-4=6 \), \( 7^{2}=49 \)
• \( 6\cdot6+49=36+49=85 \)

Answer:

1. \( 45 \)
2. \( 49 \)
3. \( 44 \)
4. \( 69 \)
5. \( 75 \)
6. \( 28 \)
7. \( 39 \)
8. \( 91 \)
9. \( 24 \)
10. \( 129 \)
11. \( 71 \)
12. \( 85 \)