Practice Maths

Topic Review — Index Notation

Mixed Practice — L01 – L04

This review covers all lessons in the Index Notation topic. Try each question before checking your answers.

Review Questions

  1. Index notation fluency. Fluency

    1. Write 8 × 8 × 8 × 8 × 8 in index notation.
    2. Evaluate: 27
    3. Evaluate: 104
    4. Write 63 in expanded form.
    5. Evaluate: 90 + 31
    6. Evaluate: 43 − 25

  2. Apply the multiplication and division index laws. Fluency

    1. 35 × 34
    2. 79 ÷ 73
    3. (53)4
    4. 26 × 23 ÷ 25
    5. (42)3 × 42
    6. 610 ÷ (63)3

  3. Negative indices and mixed index laws. Understanding

    1. Evaluate: 3−2
    2. Evaluate: 2−5
    3. Find the missing index: 5□ × 54 = 59
    4. Find the missing index: 48 ÷ 4□ = 43
    5. Is 23 × 33 = 63? Explain and verify by evaluating both sides.
    6. Simplify: (23)2 ÷ 24 × 2−1

  4. Scientific notation. Understanding

    1. Write 4 750 000 in scientific notation.
    2. Write 0.000062 in scientific notation.
    3. Write 5.3 × 106 as a standard number.
    4. Write 2.1 × 10−4 as a standard number.
    5. Arrange in ascending order: 3.8 × 105, 9.1 × 104, 4.2 × 105
    6. Calculate: (4 × 103) × (5 × 104). Give your answer in scientific notation.

  5. Mixed index and scientific notation problem solving. Problem Solving

    1. A virus cell is 2.5 × 10−7 m wide. A human hair is 7.0 × 10−5 m wide. How many times wider is the human hair than the virus cell?
    2. Simplify fully, then evaluate: [(32)3 × 3−4] ÷ 32
    3. A square room has a floor area of 46 cm². Find the side length in index notation, then evaluate in cm and convert to metres.
    4. The national debt is $9.6 × 1011. If it is shared equally among 2.4 × 107 people, how much is each person’s share? Give your answer in scientific notation and as a standard number.
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