Small practice. Bright discoveries.Explore the free starter collection
worksheetstudio.
Sign in
Back to worksheets
MathsAges 16-18

Laws of indices (exponents)

Apply the multiplication, division and power laws of indices to simplify algebraic powers. Review suitability for your learners before teaching.

New variationTry interactive challengeBrowse templates
Age band:Ages 13-15Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 16-18

Laws of indices (exponents)

Take your time. Show your thinking.

  1. 1. Simplify x^5 × x^6 in the form x^n.

    LHS=RHS
    5 · 6 · Laws of indices (exponents)

  2. 2. Simplify x^4 × x^11 in the form x^n.

    LHS=RHS
    4 · 11 · Laws of indices (exponents)

  3. 3. Simplify x^15 ÷ x^4 in the form x^n.

    LHS=RHS
    15 · 4 · Laws of indices (exponents)

  4. 4. Simplify x^11 ÷ x^5 in the form x^n.

    LHS=RHS
    11 · 5 · Laws of indices (exponents)

  5. 5. Simplify x^3 × x^3 in the form x^n.

    LHS=RHS
    3 · 3 · Laws of indices (exponents)

  6. 6. Simplify x^4 ÷ x^3 in the form x^n.

    LHS=RHS
    4 · 3 · Laws of indices (exponents)

  7. 7. Simplify x^7 ÷ x^3 in the form x^n.

    LHS=RHS
    7 · 3 · Laws of indices (exponents)

  8. 8. Simplify x^11 × x^9 in the form x^n.

    LHS=RHS
    11 · 9 · Laws of indices (exponents)

  9. 9. Simplify x^8 × x^3 in the form x^n.

    LHS=RHS
    8 · 3 · Laws of indices (exponents)

  10. 10. Simplify x^17 ÷ x^9 in the form x^n.

    LHS=RHS
    17 · 9 · Laws of indices (exponents)

  11. 11. Simplify x^20 ÷ x^8 in the form x^n.

    LHS=RHS
    20 · 8 · Laws of indices (exponents)

  12. 12. Simplify x^7 × x^11 in the form x^n.

    LHS=RHS
    7 · 11 · Laws of indices (exponents)
12 questions · Seed 104729 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Laws of indices (exponents)

Answers and reasoning. Review before teaching.

  1. 1. Simplify x^5 × x^6 in the form x^n.

    x^11

    When multiplying powers with the same base, add the exponents: 5 + 6 = 11, giving x^11.

  2. 2. Simplify x^4 × x^11 in the form x^n.

    x^15

    When multiplying powers with the same base, add the exponents: 4 + 11 = 15, giving x^15.

  3. 3. Simplify x^15 ÷ x^4 in the form x^n.

    x^11

    When dividing powers with the same base, subtract the exponents: 15 − 4 = 11, giving x^11.

  4. 4. Simplify x^11 ÷ x^5 in the form x^n.

    x^6

    When dividing powers with the same base, subtract the exponents: 11 − 5 = 6, giving x^6.

  5. 5. Simplify x^3 × x^3 in the form x^n.

    x^6

    When multiplying powers with the same base, add the exponents: 3 + 3 = 6, giving x^6.

  6. 6. Simplify x^4 ÷ x^3 in the form x^n.

    x^1

    When dividing powers with the same base, subtract the exponents: 4 − 3 = 1, giving x^1.

  7. 7. Simplify x^7 ÷ x^3 in the form x^n.

    x^4

    When dividing powers with the same base, subtract the exponents: 7 − 3 = 4, giving x^4.

  8. 8. Simplify x^11 × x^9 in the form x^n.

    x^20

    When multiplying powers with the same base, add the exponents: 11 + 9 = 20, giving x^20.

  9. 9. Simplify x^8 × x^3 in the form x^n.

    x^11

    When multiplying powers with the same base, add the exponents: 8 + 3 = 11, giving x^11.

  10. 10. Simplify x^17 ÷ x^9 in the form x^n.

    x^8

    When dividing powers with the same base, subtract the exponents: 17 − 9 = 8, giving x^8.

  11. 11. Simplify x^20 ÷ x^8 in the form x^n.

    x^12

    When dividing powers with the same base, subtract the exponents: 20 − 8 = 12, giving x^12.

  12. 12. Simplify x^7 × x^11 in the form x^n.

    x^18

    When multiplying powers with the same base, add the exponents: 7 + 11 = 18, giving x^18.

12 questions · Seed 104729 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Laws of indices (exponents)

Take your time. Show your thinking.

  1. 1. Simplify x^5 × x^6 in the form x^n.

    LHS=RHS
    5 · 6 · Laws of indices (exponents)

  2. 2. Simplify x^4 × x^11 in the form x^n.

    LHS=RHS
    4 · 11 · Laws of indices (exponents)

  3. 3. Simplify x^15 ÷ x^4 in the form x^n.

    LHS=RHS
    15 · 4 · Laws of indices (exponents)

  4. 4. Simplify x^11 ÷ x^5 in the form x^n.

    LHS=RHS
    11 · 5 · Laws of indices (exponents)

  5. 5. Simplify x^3 × x^3 in the form x^n.

    LHS=RHS
    3 · 3 · Laws of indices (exponents)

  6. 6. Simplify x^4 ÷ x^3 in the form x^n.

    LHS=RHS
    4 · 3 · Laws of indices (exponents)

  7. 7. Simplify x^7 ÷ x^3 in the form x^n.

    LHS=RHS
    7 · 3 · Laws of indices (exponents)

  8. 8. Simplify x^11 × x^9 in the form x^n.

    LHS=RHS
    11 · 9 · Laws of indices (exponents)

  9. 9. Simplify x^8 × x^3 in the form x^n.

    LHS=RHS
    8 · 3 · Laws of indices (exponents)

  10. 10. Simplify x^17 ÷ x^9 in the form x^n.

    LHS=RHS
    17 · 9 · Laws of indices (exponents)

  11. 11. Simplify x^20 ÷ x^8 in the form x^n.

    LHS=RHS
    20 · 8 · Laws of indices (exponents)

  12. 12. Simplify x^7 × x^11 in the form x^n.

    LHS=RHS
    7 · 11 · Laws of indices (exponents)
12 questions · Seed 104729 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Laws of indices (exponents)

Answers and reasoning. Review before teaching.

  1. 1. Simplify x^5 × x^6 in the form x^n.

    x^11

    When multiplying powers with the same base, add the exponents: 5 + 6 = 11, giving x^11.

  2. 2. Simplify x^4 × x^11 in the form x^n.

    x^15

    When multiplying powers with the same base, add the exponents: 4 + 11 = 15, giving x^15.

  3. 3. Simplify x^15 ÷ x^4 in the form x^n.

    x^11

    When dividing powers with the same base, subtract the exponents: 15 − 4 = 11, giving x^11.

  4. 4. Simplify x^11 ÷ x^5 in the form x^n.

    x^6

    When dividing powers with the same base, subtract the exponents: 11 − 5 = 6, giving x^6.

  5. 5. Simplify x^3 × x^3 in the form x^n.

    x^6

    When multiplying powers with the same base, add the exponents: 3 + 3 = 6, giving x^6.

  6. 6. Simplify x^4 ÷ x^3 in the form x^n.

    x^1

    When dividing powers with the same base, subtract the exponents: 4 − 3 = 1, giving x^1.

  7. 7. Simplify x^7 ÷ x^3 in the form x^n.

    x^4

    When dividing powers with the same base, subtract the exponents: 7 − 3 = 4, giving x^4.

  8. 8. Simplify x^11 × x^9 in the form x^n.

    x^20

    When multiplying powers with the same base, add the exponents: 11 + 9 = 20, giving x^20.

  9. 9. Simplify x^8 × x^3 in the form x^n.

    x^11

    When multiplying powers with the same base, add the exponents: 8 + 3 = 11, giving x^11.

  10. 10. Simplify x^17 ÷ x^9 in the form x^n.

    x^8

    When dividing powers with the same base, subtract the exponents: 17 − 9 = 8, giving x^8.

  11. 11. Simplify x^20 ÷ x^8 in the form x^n.

    x^12

    When dividing powers with the same base, subtract the exponents: 20 − 8 = 12, giving x^12.

  12. 12. Simplify x^7 × x^11 in the form x^n.

    x^18

    When multiplying powers with the same base, add the exponents: 7 + 11 = 18, giving x^18.

12 questions · Seed 104729 · Age guidance, not curriculum certification