Math Exponents

MATHS

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

 

Math Exponents

MATHS

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

 

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