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Grade 9 · Exponents
The Laws of Exponents: Complete Exam Guide
MEMORANDUM
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  / 24

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Simplify x4 · x3 (Law 1)
    (1)
    Add exponents → x7✓ (1)
  2. 2
    Simplify 3a2 · 4a5 (Law 1)
    (2)
    3 × 4 = 12, add exponents → 12a7✓✓ (2)
  3. 3
    Simplify m8 ÷ m3 (Law 2)
    (1)
    Subtract exponents → m5✓ (1)
  4. 4
    Simplify 20x6/5x2 (Law 2)
    (2)
    20 ÷ 5 = 4, subtract exponents → 4x4✓✓ (2)
  5. 5
    Simplify (a3)2 (Law 3)
    (1)
    Multiply exponents → a6✓ (1)
  6. 6
    Simplify (2y4)3 (Law 4)
    (2)
    23 = 8, and the exponents multiply: 4 × 3 = 12 → 8y12✓✓ (2)
  7. 7
    Simplify (3x2)2 (Law 4)
    (2)
    32 = 9 → 9x4✓✓ (2)
  8. 8
    Evaluate 7x0, where x ≠ 0 (Law 5)
    (1)
    x0 = 1 → 7✓ (1)
  9. 9
    Evaluate (5y)0, where y ≠ 0 (Law 5)
    (1)
    Whole bracket to power 0 → 1✓ (1)
  10. 10
    Write 4x−2 with a positive exponent (Law 6)
    (2)
    4/x2✓✓ (2)
  11. 11
    Simplify (2x3)2 · x (combined)
    (2)
    (2x3)2 = 4x6, ×x → 4x7✓✓ (2)
  12. 12
    Simplify 12a5b2/4a2b6 (combined)
    (3)
    12 ÷ 4 = 3, a5 − 2 = a3, b2 − 6 = b−4 → 3a3/b4✓✓✓ (3)
  13. 13
    Write 3 200 000 in scientific notation
    (2)
    3,2 × 106✓✓ (2)
  14. 14
    Write 0,0007 in scientific notation
    (2)
    Small number → negative power → 7 × 10−4✓✓ (2)
TOTAL: 24 marks
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