Skip to main content
Ecolint Campus des NationsMathematics
← Review packs

Pack A — Fluency

Ecolint Campus des NationsMathematics
Year 9 · 9.7 Indices and Scientific Notation

Pack A · Fluency

Name: _________________________________
Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10
  1. 1.
    Evaluate 252^5.
     
  2. 2.
    Write 32×353^2 \times 3^5 as a single power of aa.
     
  3. 3.
    Write apaq\dfrac{a^p}{a^q} as a single power.
     
  4. 4.
    Write 32000 in standard form.
     
  5. 5.
    Write the decimal 0.004 in standard form.
     
  6. 6.
    Evaluate (7)0(7)^0 and (7)−2(7)^{-2}.
     
  7. 7.
    Write (ap)q(a^p)^q as a single power.
     
  8. 8.
    Simplify xp×xqx^p \times x^q.
     
  9. 9.
    Write 0.5 × 10⁵ in standard form.
     
  10. 10.
    Evaluate 505^0 and 515^1.
     
SilverQuestions 11–20
  1. 11.
    Simplify (a×10p)×(b×10q)(a \times 10^p) \times (b \times 10^q).
     
  2. 12.
    Simplify a×10pb×10q\dfrac{a \times 10^p}{b \times 10^q}.
     
  3. 13.
    Simplify xpxq\dfrac{x^p}{x^q}.
     
  4. 14.
    Evaluate a1/2a^{1/2}.
     
  5. 15.
    Write 35×10535 \times 10^5 in standard form.
     
  6. 16.
    Compute 5×104+3×1035 \times 10^4 + 3 \times 10^3 in standard form.
     
  7. 17.
    Evaluate a−1a^{-1}.
     
  8. 18.
    Simplify (2x)3(2x)^3.
     
  9. 19.
    Convert: a light-year ≈ 9.5×10129.5 \times 10^{12} km. Express in metres.
     
  10. 20.
    Compute (2×103)2(2 \times 10^3)^2.
     
GoldQuestions 21–30
  1. 21.
    Simplify (xp)qxr\dfrac{(x^p)^q}{x^r}.
     
  2. 22.
    Write 35×10535 \times 10^5 in standard form.
     
  3. 23.
    Evaluate a1/2a^{1/2} where a = 25.
     
  4. 24.
    UK population was 6.50×1076.50 \times 10^7 in 2016, growing 0.6% per year. Estimate the 2020 population (3 s.f.).
     
  5. 25.
    Compute (3×104)×(4×10−2)(3 \times 10^4) \times (4 \times 10^{-2}) in standard form.
     
  6. 26.
    Convert a×10pa \times 10^p to ordinary: 3.6×10−33.6 \times 10^{-3}.
     
  7. 27.
    Evaluate a2/3a^{2/3} where a = 8.
     
  8. 28.
    Compute 6×1072×104\dfrac{6 \times 10^7}{2 \times 10^4} in standard form.
     
  9. 29.
    Simplify (2x3)2×(3x)2(2x^3)^2 \times (3x)^2.
     
  10. 30.
    Order from smallest to largest: 3×10−3,2×10−4,4×10−33 \times 10^{-3}, 2 \times 10^{-4}, 4 \times 10^{-3}.
     
PlatinumQuestions 31–40
  1. 31.
    Solve xp=rhsx^p = {rhs}.
     
  2. 32.
    Evaluate a−1/2a^{-1/2}.
     
  3. 33.
    A nearby star is 4.24.2 light-years away. 1 light-year ≈ 9.46×10129.46 \times 10^{12} km. Find distance in km (3 s.f.).
     
  4. 34.
    Solve x1/3=nx^{1/3} = n.
     
  5. 35.
    A bacteria culture starts at 2.5×1042.5 \times 10^4 cells, doubling every hour. (a) After 1 hour. (b) After 5 hours. (c) When does it exceed 10810^8?
     
  6. 36.
    Evaluate 27−2/327^{-2/3}.
     
  7. 37.
    Solve 2x=322^x = 32.
     
  8. 38.
    Solve x4=81x^4 = 81 for real xx.
     
  9. 39.
    Express 27a93\sqrt[3]{27 a^9} in simplified index form.
     
  10. 40.
    Compute (103)1/3(10^3)^{1/3} and (106)1/3(10^6)^{1/3}.