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MathsAges 13-15

Laws of indices (exponents)

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

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Age band:Ages 13-15Ages 16-18

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Worksheet StudioPractice pack · Ages 13-15

Laws of indices (exponents)

Take your time. Show your thinking.

  1. 1. Simplify x^5 × x^12 in the form x^n.

    LHS=RHS
    5 · 12 · Laws of indices (exponents)

  2. 2. Simplify x^2 × x^10 in the form x^n.

    LHS=RHS
    2 · 10 · Laws of indices (exponents)

  3. 3. Simplify x^16 ÷ x^5 in the form x^n.

    LHS=RHS
    16 · 5 · Laws of indices (exponents)

  4. 4. Simplify x^6 × x^2 in the form x^n.

    LHS=RHS
    6 · 2 · Laws of indices (exponents)

  5. 5. Simplify x^4 × x^5 in the form x^n.

    LHS=RHS
    4 · 5 · Laws of indices (exponents)

  6. 6. Simplify x^10 × x^6 in the form x^n.

    LHS=RHS
    10 · 6 · Laws of indices (exponents)

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

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

  8. 8. Simplify x^14 ÷ x^9 in the form x^n.

    LHS=RHS
    14 · 9 · Laws of indices (exponents)

  9. 9. Simplify x^12 ÷ x^4 in the form x^n.

    LHS=RHS
    12 · 4 · Laws of indices (exponents)

  10. 10. Simplify x^20 ÷ x^9 in the form x^n.

    LHS=RHS
    20 · 9 · Laws of indices (exponents)

  11. 11. Simplify x^3 ÷ x^2 in the form x^n.

    LHS=RHS
    3 · 2 · Laws of indices (exponents)

  12. 12. Simplify x^21 ÷ x^10 in the form x^n.

    LHS=RHS
    21 · 10 · Laws of indices (exponents)
12 questions · Seed 44 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Laws of indices (exponents)

Answers and reasoning. Review before teaching.

  1. 1. Simplify x^5 × x^12 in the form x^n.

    x^17

    When multiplying powers with the same base, add the exponents: 5 + 12 = 17, giving x^17.

  2. 2. Simplify x^2 × x^10 in the form x^n.

    x^12

    When multiplying powers with the same base, add the exponents: 2 + 10 = 12, giving x^12.

  3. 3. Simplify x^16 ÷ x^5 in the form x^n.

    x^11

    When dividing powers with the same base, subtract the exponents: 16 − 5 = 11, giving x^11.

  4. 4. Simplify x^6 × x^2 in the form x^n.

    x^8

    When multiplying powers with the same base, add the exponents: 6 + 2 = 8, giving x^8.

  5. 5. Simplify x^4 × x^5 in the form x^n.

    x^9

    When multiplying powers with the same base, add the exponents: 4 + 5 = 9, giving x^9.

  6. 6. Simplify x^10 × x^6 in the form x^n.

    x^16

    When multiplying powers with the same base, add the exponents: 10 + 6 = 16, giving x^16.

  7. 7. 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.

  8. 8. Simplify x^14 ÷ x^9 in the form x^n.

    x^5

    When dividing powers with the same base, subtract the exponents: 14 − 9 = 5, giving x^5.

  9. 9. Simplify x^12 ÷ x^4 in the form x^n.

    x^8

    When dividing powers with the same base, subtract the exponents: 12 − 4 = 8, giving x^8.

  10. 10. Simplify x^20 ÷ x^9 in the form x^n.

    x^11

    When dividing powers with the same base, subtract the exponents: 20 − 9 = 11, giving x^11.

  11. 11. Simplify x^3 ÷ x^2 in the form x^n.

    x^1

    When dividing powers with the same base, subtract the exponents: 3 − 2 = 1, giving x^1.

  12. 12. Simplify x^21 ÷ x^10 in the form x^n.

    x^11

    When dividing powers with the same base, subtract the exponents: 21 − 10 = 11, giving x^11.

12 questions · Seed 44 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Laws of indices (exponents)

Take your time. Show your thinking.

  1. 1. Simplify x^5 × x^12 in the form x^n.

    LHS=RHS
    5 · 12 · Laws of indices (exponents)

  2. 2. Simplify x^2 × x^10 in the form x^n.

    LHS=RHS
    2 · 10 · Laws of indices (exponents)

  3. 3. Simplify x^16 ÷ x^5 in the form x^n.

    LHS=RHS
    16 · 5 · Laws of indices (exponents)

  4. 4. Simplify x^6 × x^2 in the form x^n.

    LHS=RHS
    6 · 2 · Laws of indices (exponents)

  5. 5. Simplify x^4 × x^5 in the form x^n.

    LHS=RHS
    4 · 5 · Laws of indices (exponents)

  6. 6. Simplify x^10 × x^6 in the form x^n.

    LHS=RHS
    10 · 6 · Laws of indices (exponents)

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

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

  8. 8. Simplify x^14 ÷ x^9 in the form x^n.

    LHS=RHS
    14 · 9 · Laws of indices (exponents)

  9. 9. Simplify x^12 ÷ x^4 in the form x^n.

    LHS=RHS
    12 · 4 · Laws of indices (exponents)

  10. 10. Simplify x^20 ÷ x^9 in the form x^n.

    LHS=RHS
    20 · 9 · Laws of indices (exponents)

  11. 11. Simplify x^3 ÷ x^2 in the form x^n.

    LHS=RHS
    3 · 2 · Laws of indices (exponents)

  12. 12. Simplify x^21 ÷ x^10 in the form x^n.

    LHS=RHS
    21 · 10 · Laws of indices (exponents)
12 questions · Seed 44 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Laws of indices (exponents)

Answers and reasoning. Review before teaching.

  1. 1. Simplify x^5 × x^12 in the form x^n.

    x^17

    When multiplying powers with the same base, add the exponents: 5 + 12 = 17, giving x^17.

  2. 2. Simplify x^2 × x^10 in the form x^n.

    x^12

    When multiplying powers with the same base, add the exponents: 2 + 10 = 12, giving x^12.

  3. 3. Simplify x^16 ÷ x^5 in the form x^n.

    x^11

    When dividing powers with the same base, subtract the exponents: 16 − 5 = 11, giving x^11.

  4. 4. Simplify x^6 × x^2 in the form x^n.

    x^8

    When multiplying powers with the same base, add the exponents: 6 + 2 = 8, giving x^8.

  5. 5. Simplify x^4 × x^5 in the form x^n.

    x^9

    When multiplying powers with the same base, add the exponents: 4 + 5 = 9, giving x^9.

  6. 6. Simplify x^10 × x^6 in the form x^n.

    x^16

    When multiplying powers with the same base, add the exponents: 10 + 6 = 16, giving x^16.

  7. 7. 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.

  8. 8. Simplify x^14 ÷ x^9 in the form x^n.

    x^5

    When dividing powers with the same base, subtract the exponents: 14 − 9 = 5, giving x^5.

  9. 9. Simplify x^12 ÷ x^4 in the form x^n.

    x^8

    When dividing powers with the same base, subtract the exponents: 12 − 4 = 8, giving x^8.

  10. 10. Simplify x^20 ÷ x^9 in the form x^n.

    x^11

    When dividing powers with the same base, subtract the exponents: 20 − 9 = 11, giving x^11.

  11. 11. Simplify x^3 ÷ x^2 in the form x^n.

    x^1

    When dividing powers with the same base, subtract the exponents: 3 − 2 = 1, giving x^1.

  12. 12. Simplify x^21 ÷ x^10 in the form x^n.

    x^11

    When dividing powers with the same base, subtract the exponents: 21 − 10 = 11, giving x^11.

12 questions · Seed 44 · Age guidance, not curriculum certification