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Year 9 Mathematics · Index laws

Name: ______________________

Date: ____________

  1. 1. Simplify 2^3 × 2^4.

    • ☐ (a) 2^7
    • ☐ (b) 2^12
    • ☐ (c) 4^7
    • ☐ (d) 2^1

  2. 2. Simplify y^9 ÷ y^3.

    • ☐ (a) y^3
    • ☐ (b) y^6
    • ☐ (c) y^27
    • ☐ (d) y^12

  3. 3. Simplify (x^2)^5.

    • ☐ (a) x^7
    • ☐ (b) x^25
    • ☐ (c) x^10
    • ☐ (d) 2x^5

  4. 4. What is the value of 7^0?

    • ☐ (a) 0
    • ☐ (b) 7
    • ☐ (c) 70
    • ☐ (d) 1

  5. 5. Simplify (3a)^2.

    • ☐ (a) 3a^2
    • ☐ (b) 6a
    • ☐ (c) 9a^2
    • ☐ (d) 9a

  6. 6. Evaluate 5^0 + 2^3.

  7. 7. Simplify 6x^5 × 2x^3. Write powers using ^, for example x^2.

  8. 8. Write 3^4 as an ordinary number.

Answer sheet

  1. 1. 2^7 — Same base, so add the indices: 3 + 4 = 7. The answer is 2^7.
  2. 2. y^6 — Same base, so subtract the indices: 9 − 3 = 6. The answer is y^6.
  3. 3. x^10 — For a power of a power, multiply the indices: 2 × 5 = 10. The answer is x^10.
  4. 4. 1 — Any non-zero number raised to the power of 0 equals 1.
  5. 5. 9a^2 — Both factors inside the bracket are squared: 3^2 × a^2 = 9a^2.
  6. 6. 9 — 5^0 = 1 and 2^3 = 8, so the total is 1 + 8 = 9.
  7. 7. 12x^8 — Multiply the coefficients (6 × 2 = 12) and add the indices (5 + 3 = 8) to get 12x^8.
  8. 8. 81 — 3^4 = 3 × 3 × 3 × 3 = 9 × 9 = 81.

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