Exponents Worksheet

Name: _________________________ Date: _______________

Part 1: Basic Exponents

1. Write the following in exponential form:
    
   • a) 3 × 3 × 3 × 3 = ___________
   • b) 7 × 7 = ___________
   • c) 2 × 2 × 2 × 2 × 2 × 2 = ___________
   • d) 5 × 5 × 5 = ___________
2. Evaluate the following:
    
   • a) 2³ = ___________
   • b) 4² = ___________
   • c) 10¹ = ___________
   • d) 3⁴ = ___________
   • e) 1⁸ = ___________
   • f) 6² = ___________

Part 2: Multiplication of Exponents (Same Base)

1. Simplify the following using the rule aᵐ × aⁿ = aᵐ⁺ⁿ:
    
   • a) 2² × 2³ = ___________
   • b) 5¹ × 5⁴ = ___________
   • c) x³ × x⁵ = ___________
   • d) a² × a⁷ = ___________
2. Evaluate after simplifying:
    
   • a) 3² × 3¹ = ___________
   • b) 2⁴ × 2² = ___________

Part 3: Division of Exponents (Same Base)

1. Simplify the following using the rule aᵐ ÷ aⁿ = aᵐ⁻ⁿ:
    
   • a) 5⁵ ÷ 5² = ___________
   • b) 7⁶ ÷ 7³ = ___________
   • c) x⁸ ÷ x⁴ = ___________
   • d) a⁹ ÷ a⁶ = ___________
2. Evaluate after simplifying:
    
   • a) 2⁵ ÷ 2³ = ___________
   • b) 3⁴ ÷ 3² = ___________

Part 4: Power of a Power

1. Simplify the following using the rule (aᵐ)ⁿ = aᵐ ˣ ⁿ:
    
   • a) (2³) ² = ___________
   • b) (5²) ⁴ = ___________
   • c) (x⁴) ³ = ___________
   • d) (a⁵) ² = ___________
2. Evaluate after simplifying:
    
   • a) (3²) ² = ___________
   • b) (2³) ³ = ___________

Part 5: Zero and Negative Exponents

1. Evaluate:
    
   • a) 6⁰ = ___________
   • b) 12⁰ = ___________
   • c) x⁰ = ___________ (where x ≠ 0)
   • d) 5⁻¹ = ___________
   • e) 2⁻³ = ___________
   • f) 10⁻² = ___________
2. Simplify and then evaluate if possible.
    
   • a) 4³ × 4⁻¹ = ___________
   • b) 3⁻² × 3⁴ = ___________

Answer Key:

Part 1: Basic Exponents

• a) 3⁴
• b) 7²
• c) 2⁶
• d) 5³
• a) 8
• b) 16
• c) 10
• d) 81
• e) 1
• f) 36

Part 2: Multiplication of Exponents (Same Base)

• a) 2⁵
• b) 5⁵
• c) x⁸
• d) a⁹
• a) 27
• b) 64

Part 3: Division of Exponents (Same Base)

• a) 5³
• b) 7³
• c) x⁴
• d) a³
• a) 4
• b) 9

Part 4: Power of a Power

• a) 2⁶
• b) 5⁸
• c) x¹²
• d) a¹⁰
• a) 81
• b) 512

Part 5: Zero and Negative Exponents

• a) 1
• b) 1
• c) 1
• d) 1/5
• e) 1/8
• f) 1/100
• a) 4² = 16
• b) 3² = 9