Let’s solve each problem step by step. Remember: when you see a number with an exponent, like \(9^3\), it means multiply 9 by itself 3 times: \(9 \times 9 \times 9\). Also, if there’s a negative sign inside parentheses like \((-9)^2\), the negative is part of what gets squared. But if it’s written as \(-9^2\) without parentheses, only the 9 is squared, and then you make it negative.
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Problem 1: \((-9)^0 + 3^4\)
- Any number (except 0) to the power of 0 is 1 → \((-9)^0 = 1\)
- \(3^4 = 3 \times 3 \times 3 \times 3 = 81\)
- Add them: \(1 + 81 = 82\)
✔ Answer:
82
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Problem 2: \((-9)^2 + (-7)^2\)
- \((-9)^2 = (-9) \times (-9) = 81\)
- \((-7)^2 = (-7) \times (-7) = 49\)
- Add: \(81 + 49 = 130\)
✔ Answer:
130
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Problem 3: \(10^{-2} + (-9)^2\)
- \(10^{-2} = \frac{1}{10^2} = \frac{1}{100} = 0.01\)
- \((-9)^2 = 81\)
- Add: \(0.01 + 81 = 81.01\)
✔ Answer:
81.01
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Problem 4: \(9^3 + (-9)^0\)
- \(9^3 = 9 \times 9 \times 9 = 729\)
- \((-9)^0 = 1\)
- Add: \(729 + 1 = 730\)
✔ Answer:
730
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Problem 5: \(4^2 + (-6)^3\)
- \(4^2 = 16\)
- \((-6)^3 = (-6) \times (-6) \times (-6) = 36 \times (-6) = -216\)
- Add: \(16 + (-216) = -200\)
✔ Answer:
-200
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Problem 6: \(-9^2 + 3^3\)
⚠️ Important: This is NOT \((-9)^2\). It’s “negative of 9 squared”.
- \(9^2 = 81\), so \(-9^2 = -81\)
- \(3^3 = 27\)
- Add: \(-81 + 27 = -54\)
✔ Answer:
-54
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Problem 7: \(4^0 + 8^0\)
- Any non-zero number to the 0 power is 1 → \(4^0 = 1\), \(8^0 = 1\)
- Add: \(1 + 1 = 2\)
✔ Answer:
2
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Problem 8: \(-3^0 + (-8)^2\)
- \(3^0 = 1\), so \(-3^0 = -1\)
- \((-8)^2 = 64\)
- Add: \(-1 + 64 = 63\)
✔ Answer:
63
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Problem 9: \(8^4 + 2^3\)
- \(8^4 = 8 \times 8 \times 8 \times 8 = 4096\)
- \(2^3 = 8\)
- Add: \(4096 + 8 = 4104\)
✔ Answer:
4104
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Problem 10: \((-2)^4 + (-0.02)^2\)
- \((-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16\)
- \((-0.02)^2 = (-0.02) \times (-0.02) = 0.0004\)
- Add: \(16 + 0.0004 = 16.0004\)
✔ Answer:
16.0004
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Final Answer:
1. 82
2. 130
3. 81.01
4. 730
5. -200
6. -54
7. 2
8. 63
9. 4104
10. 16.0004
Parent Tip: Review the logic above to help your child master the concept of free printable algebra 1 worksheet.
