Practice Maths

Power of a Power Law — Solutions

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  1. Power of a power law

  2. Mixed all three laws

  3. Multiple laws in sequence

    1. (23)2 × (22)3:
    2. [(32)3 ÷ 34] × 32:
    3. (54)2 ÷ [(53)2 × 5]:
    4. (102)4 × 103 ÷ (105)2:
    5. [(72)3 × 74] ÷ (75)2:
    6. (43)2 ÷ (42)2 × 41:
    7. (62)4 ÷ [(63)2 × 62]:
    8. (93)2 × (92)3 ÷ 910:

  4. Negative indices

    1. 2−1:
    2. 3−2:
    3. 5−1:
    4. 4−2:
    5. 10−3:
    6. 2−4:
    7. 6−2:
    8. 3−3:

  5. Which law?

    1. 53 × 54 = 57:
    2. (24)3 = 212:
    3. 79 ÷ 74 = 75:
    4. (32)4 × 32:
    5. 68 ÷ (62)3:
    6. (45)2 ÷ (43)3:

  6. Problem solving

    1. Distance to star:
    2. 2−3 grams:
    3. (23)2 ÷ (22)2 × 22:
    4. Priya’s mistake:
    5. (23)2 × 24 ÷ (25)2:

  7. Power of a power with evaluation

    1. (22)3:
    2. (31)4:
    3. (102)2:
    4. (23)3:
    5. (52)2:
    6. (41)5:
    7. (25)1:
    8. (32)2:

  8. Identify which law(s), then simplify

    1. 34 × 35:
    2. (43)3:
    3. 67 ÷ 64:
    4. (25)2 × 23:
    5. 59 ÷ (53)2:
    6. 72 × (72)4:
    7. (84)0:
    8. (92)3 ÷ 95:

  9. Find the missing index

    1. (3□)4 = 38:
    2. (53)□ = 515:
    3. (2□)3 = 212:
    4. (72)□ = 710:
    5. (4□)5 = 420:
    6. (63)□ = 69:

  10. Multi-law challenge

    1. Square garden:
    2. (43)2 ÷ 44:
    3. (34)3 vs (33)4:
    4. Expressions equal to 212: