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Quiz: Surds And Indices

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Number of Questions: 25

Question: 6 -

(3a+1 9a+2 27a) / (3a-1 9a 27a+1) = ?

Options:

  1. 1

  2. 3

  3. 9

  4. 27

    5. Answer:

    27
    Solution:

    (3a+1 9a+2 27a) / (3a-1 9a 27a+1) = [3a+1 32(a+2) (33)a] / [3a-1 (32)a (33)a+1] = 36a+5 / 36a+2 = 33 = 27.

Question: 7 -

(3-3 * 95/2) / (272/3 * 3-4) = ?

Options:

  1. 21

  2. 3

  3. 9

  4. 81

    5. Answer:

    81
    Solution:

    (3-3 * 95/2) / (272/3 * 3-4) = [3-3 * (32)5/2] / [(33)2/3 * 3-4] 

    = (3-3 * 35) / (32 * 3-4) = (3-3+5)/(32-4) = 32/3-2 = 32 * 32 = 81. 

Question: 8 -

(1714 * 1716) / 17-8 = ?

Options:

  1. 1728

  2. 1722

  3. 1724

  4. 1726

    5. Answer:

    1722
    Solution:

    ? = 1714+16-8 = 1722

Question: 9 -

(272/3 * 91/2 * 811/4)-1/4 = ?

Options:

  1. 1/3

  2. 1/9

  3. 9

  4. 3

    5. Answer:

    1/3
    Solution:

    (272/3 * 91/2 * 811/4)-1/4 = [(33)2/3 * (32)1/2 * (34)1/4]-1/4 

    = (32 * 3 * 3)-1/4 = (34)-1/4 = 1/3.

Question: 10 -

(9-7 / 27-3)4/5 = ?

Options:

  1. 3-1

  2. 3-2

  3. 3-4

  4. 3-3

    5. Answer:

    3-4
    Solution:

    (9-7 / 27-3)4/5 = [(32)-7 / (33)-3]4/5 

    = (3-14 39)4/5 = 3-4 .