Let’s go through each problem one by one using the laws of exponents. I’ll explain what rule we’re using for each, then give the answer.
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1) 3⁰ = ?
Any number (except 0) raised to the power of 0 is 1.
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Answer: 1
2) 3³ × 3⁻⁵ = ?
When multiplying powers with the same base, add the exponents: 3 + (-5) = -2
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Answer: 3⁻²
3) (¹/₇)³ = ?
Raise both numerator and denominator to the power: 1³ / 7³ = 1 / 7³
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Answer: ¹/₇³
4) (7 × 2)² = ?
Distribute the exponent to each factor inside: 7² × 2²
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Answer: 7² × 2²
5) (8 × 3)⁹ = ?
Same as above — distribute the exponent: 8⁹ × 3⁹
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Answer: 8⁹ × 3⁹
6) (¹/₄)⁸ = ?
Raise top and bottom to the 8th power: 1⁸ / 4⁸ = 1 / 4⁸
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Answer: ¹/₄⁸
7) 8⁰ = ?
Anything to the 0 power is 1.
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Answer: 1
8) 7⁸ × 7⁵ = ?
Add exponents: 8 + 5 = 13 → 7¹³
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Answer: 7¹³
9) 5³ × 5² = ?
Add exponents: 3 + 2 = 5 → 5⁵
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Answer: 5⁵
10) 4⁻⁸ = ?
Negative exponent means flip it to a fraction: 1 / 4⁸
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Answer: ¹/₄⁸
11) 7¹ = ?
Any number to the 1st power is itself.
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Answer: 7
12) (8 × 6)⁹ = ?
Distribute the exponent: 8⁹ × 6⁹
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Answer: 8⁹ × 6⁹
13) 4⁸ × 4⁻⁷ = ?
Add exponents: 8 + (-7) = 1 → 4¹
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Answer: 4¹
14) 4⁴ × 4³ = ?
Add exponents: 4 + 3 = 7 → 4⁷
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Answer: 4⁷
15) (8⁴)³ = ?
Power of a power — multiply exponents: 4 × 3 = 12 → 8¹²
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Answer: 8¹²
16) 6³ × 6⁻⁹ = ?
Add exponents: 3 + (-9) = -6 → 6⁻⁶
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Answer: 6⁻⁶
17) 3⁰ = ?
Again, anything to the 0 power is 1.
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Answer: 1
18) 6¹ = ?
To the first power? Just the number itself.
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Answer: 6
19) 8⁻⁵ = ?
Negative exponent → flip to fraction: 1 / 8⁵
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Answer: ¹/₈⁵
20) (5³)⁵ = ?
Multiply exponents: 3 × 5 = 15 → 5¹⁵
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Answer: 5¹⁵
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Final Answer:
1. 1
2. 3⁻²
3. ¹/₇³
4. 7² × 2²
5. 8⁹ × 3⁹
6. ¹/₄⁸
7. 1
8. 7¹³
9. 5⁵
10. ¹/₄⁸
11. 7
12. 8⁹ × 6⁹
13. 4¹
14. 4⁷
15. 8¹²
16. 6⁻⁶
17. 1
18. 6
19. ¹/₈⁵
20. 5¹⁵
Parent Tip: Review the logic above to help your child master the concept of laws of exponents worksheet 8th grade.
