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Ecolint Campus des NationsMathematics
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Pack A — Fluency

Ecolint Campus des NationsMathematics
Year 10 · Exponents and Indices

Pack A · Fluency

Name: _________________________________
Date: _________________ Class: ___________

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

BronzeQuestions 1–10
  1. 1.
    Evaluate 2exp2^{{exp}}.
     
  2. 2.
    Evaluate 707^{0}.
     
  3. 3.
    Simplify xa×xbx^{{a}} \times x^{{b}}.
     
  4. 4.
    Simplify xaxb\dfrac{x^{{a}}}{x^{{b}}}.
     
  5. 5.
    Simplify (xa)b(x^{{a}})^{{b}}.
     
  6. 6.
    Simplify (2xp)2(2 x^{{p}})^2.
     
  7. 7.
    Write 2−exp2^{-{exp}} as a fraction.
     
  8. 8.
    Write 30003000 in standard form (scientific notation).
     
  9. 9.
    Write 0.0040.004 in standard form.
     
  10. 10.
    Write 2.5×10p2.5 \times 10^{{p}} as an ordinary number.
     
SilverQuestions 11–20
  1. 11.
    Simplify 3xp×4xq3 x^{{p}} \times 4 x^{{q}}.
     
  2. 12.
    Simplify c1xpc2xq\dfrac{{c1} x^{{p}}}{{c2} x^{{q}}}.
     
  3. 13.
    Simplify (xaxb)n\left(\dfrac{x^{{a}}}{x^{{b}}}\right)^{{n}}.
     
  4. 14.
    Simplify xa×x−bx^{{a}} \times x^{-{b}}.
     
  5. 15.
    Write 1xn\dfrac{1}{x^{{n}}} using a negative index.
     
  6. 16.
    Calculate (3×10p)×(2×10q)(3 \times 10^{{p}}) \times (2 \times 10^{{q}}), giving your answer in standard form.
     
  7. 17.
    Calculate a×10pb×10q\dfrac{{a} \times 10^{{p}}}{{b} \times 10^{{q}}} in standard form.
     
  8. 18.
    Simplify xa×xbxc\dfrac{x^{{a}} \times x^{{b}}}{x^{{c}}}.
     
  9. 19.
    How many times larger is 6×10p6 \times 10^{{p}} than 2×10q2 \times 10^{{q}}?
     
  10. 20.
    Simplify (−3xp)n(-3 x^{{p}})^{{n}}.
     
GoldQuestions 21–30
  1. 21.
    Evaluate 251/225^{1/2}.
     
  2. 22.
    Evaluate 271/327^{1/3}.
     
  3. 23.
    Evaluate 82/38^{2/3}.
     
  4. 24.
    Evaluate 16−1/216^{-1/2}.
     
  5. 25.
    Simplify (cxa)nxb\dfrac{({c} x^{{a}})^{{n}}}{x^{{b}}}.
     
  6. 26.
    Calculate (3×10p)+(5×10q)(3 \times 10^{{p}}) + (5 \times 10^{{q}}) in standard form.
     
  7. 27.
    Simplify (8)−2/3(8)^{-2/3}.
     
  8. 28.
    Solve 2x=322^x = 32.
     
  9. 29.
    If x=12x = \dfrac{1}{2}, evaluate xpx^{{p}}.
     
  10. 30.
    Write xm3\sqrt[3]{x^{{m}}} using a fractional index.
     
PlatinumQuestions 31–40
  1. 31.
    Solve 2x+1=322^{x+1} = 32.
     
  2. 32.
    Solve 32x=813^{2x} = 81.
     
  3. 33.
    Simplify (cxa)n⋅xbxc2\dfrac{({c} x^{{a}})^{{n}} \cdot x^{{b}}}{x^{{c2}}}.
     
  4. 34.
    The mass of Earth is 6×10246 \times 10^{24} kg and the mass of the Sun is 2×10p2 \times 10^{{p}} kg. How many times more massive is the Sun?
     
  5. 35.
    Simplify xa⋅y−bx−c⋅yd\dfrac{x^{{a}} \cdot y^{-{b}}}{x^{-{c}} \cdot y^{{d}}}, expressing the answer with positive indices.
     
  6. 36.
    Evaluate (16)3/4(16)^{3/4}.
     
  7. 37.
    Light travels at 3×1083 \times 10^8 m/s. Calculate the distance light travels in 600600 seconds, in standard form.
     
  8. 38.
    Solve 2x⋅2x+1=322^{x} \cdot 2^{x+1} = 32.
     
  9. 39.
    Simplify (cxaybxc2yd)n\left(\dfrac{{c}x^{{a}}y^{{b}}}{x^{{c2}}y^{{d}}}\right)^{{n}}.
     
  10. 40.
    Solve x1/3=4x^{1/3} = 4 for positive xx.