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About Exponents & Powers — Class 8 ICSE

Apply laws of exponents to simplify expressions with negative and zero exponents. This topic is part of the ICSE Class 8 mathematics syllabus (chapter: Chapter 2). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Exponents & Powers

  • Understanding Exponents
  • Laws of Exponents
  • Negative Exponents
  • Standard Form (Scientific Notation)
  • Comparing Powers and Review

Interactive lesson · about 20 minutes · checkpoint question after every unit

Exponents & Powers — solved examples for Class 8 ICSE

Example 1easy

What is 2⁵?
  1. A)10
  2. B)16
  3. C)32
  4. D)64

Step-by-step solution

  1. 2⁵ means:
    2×2×2×2×22 × 2 × 2 × 2 × 2
  2. Calculate step by step:
    4×4×2=324 × 4 × 2 = 32

Answer: 32

Example 2medium

Simplify: 2⁵ × 3⁵
  1. A)6⁵
  2. B)6¹⁰
  3. C)5⁶
  4. D)6²⁵

Step-by-step solution

  1. Law:
    an×bn=(a×b)naⁿ × bⁿ = (a × b)ⁿ
  2. Apply:
    25×35=(2×3)5=652⁵ × 3⁵ = (2 × 3)⁵ = 6⁵

Answer: 6⁵

Example 3hard

If 2ˣ⁺¹ + 2ˣ = 48, find x.
  1. A)3
  2. B)4
  3. C)5
  4. D)6

Step-by-step solution

  1. Factor:
    2x(21+1)=482ˣ(2¹ + 1) = 48
  2. Simplify:
    2x×3=482ˣ × 3 = 48
  3. Solve:
    2x=16=242ˣ = 16 = 2⁴
  4. Therefore:
    x=4x = 4

Answer: 4

Practice questions on Exponents & Powers

  1. Q1.easy

    Simplify: 3² × 3³
    1. A)3⁵
    2. B)3⁶
    3. C)9⁵
    4. D)9⁶
    Show answer

    Answer: 3⁵

    Hint: When multiplying powers with the same base, add the exponents.

  2. Q2.easy

    What is the value of 5⁰?
    1. A)0
    2. B)1
    3. C)5
    4. D)Undefined
    Show answer

    Answer: 1

    Hint: Any non-zero number raised to the power 0 equals a specific value.

  3. Q3.easy

    Simplify: 7⁸ ÷ 7⁵
    1. A)7³
    2. B)7¹³
    3. C)1³
    4. D)7⁴⁰
    Show answer

    Answer: 7³

    Hint: When dividing powers with the same base, subtract the exponents.

  4. Q4.medium

    Simplify: (2³ × 4²) ÷ 2⁵
    1. A)2²
    2. B)2³
    3. C)4
    4. D)8
    Show answer

    Answer: 2²

    Hint: Express 4 as 2² first, then use laws of exponents.

  5. Q5.medium

    Find the value of: 3⁻² × 3⁴ × 3⁻¹
    1. A)3
    2. B)9
    3. C)27
    4. D)1/3
    Show answer

    Answer: 3

    Hint: Add all the exponents (including negatives) since the base is the same.

  6. Q6.medium

    Evaluate: (2/3)⁻² × (3/2)²
    1. A)1
    2. B)81/16
    3. C)9/4
    4. D)4/9
    Show answer

    Answer: 81/16

    Hint: (2/3)⁻² = (3/2)². Then multiply.

  7. Q7.hard

    Simplify: (3⁻² × 3⁴ × 3⁻¹)² ÷ (3² × 3⁻³)³
    1. A)3⁵
    2. B)243
    3. C)3
    4. D)27
    Show answer

    Answer: 3⁵

    Hint: Simplify inside each bracket first, then apply external powers.

  8. Q8.hard

    If 9ⁿ × 3² × (3⁻ⁿ/²)⁻² = 27, find n.
    1. A)1/2
    2. B)1
    3. C)3/2
    4. D)2
    Show answer

    Answer: 1/2

    Hint: Express everything as powers of 3.

  9. Q9.hard

    Simplify: (xᵃ/xᵇ)ᵃ⁺ᵇ × (xᵇ/xᶜ)ᵇ⁺ᶜ × (xᶜ/xᵃ)ᶜ⁺ᵃ
    1. A)x
    2. B)1
    3. C)x²
    4. D)xᵃᵇᶜ
    Show answer

    Answer: 1

    Hint: Simplify each fraction first, then apply the power using (xᵐ)ⁿ = xᵐⁿ.

These are 9 of the 60 questions available for Exponents & Powers. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.