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Grade 11 · Exponents and Surds
Exponent Laws & Exponential Equations (Grade 11)
MEMORANDUM
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Class: 
Date: 
Mark
  / 20

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 163/4
    (2)
    (4th root of 16)³ = 2³ = 8✓✓ (2)
  2. 2
    Simplify 2−3
    (1)
    1/8✓ (1)
  3. 3
    Simplify (9n × 3n + 1)/27n
    (3)
    32n + n + 1 − 3n = 31 = 3✓✓✓ (3)
  4. 4
    Solve for x: 3x + 2 = 81
    (2)
    3x + 2 = 34 → x = 2✓✓ (2)
  5. 5
    Solve for x: 52x − 1 = 125
    (2)
    2x − 1 = 3 → x = 2✓✓ (2)
  6. 6
    Solve for x: 22x − 5(2x) + 4 = 0
    (4)
    Let k = 2x: (k − 1)(k − 4) = 0 → x = 0 or x = 2✓✓✓✓ (4)
  7. 7
    Solve for x: 32x − 4(3x) + 3 = 0
    (4)
    (k − 1)(k − 3) = 0 → x = 0 or x = 1✓✓✓✓ (4)
  8. 8
    Simplify 82/3
    (2)
    (cube root of 8)² = 2² = 4✓✓ (2)
TOTAL: 20 marks
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